Author: Iñigo Careaga, strategy & communication manager, CIC energiGUNE

Lithium and sodium are neighbours in the periodic table. Both are alkali metals, both have a single electron in their outer shell, and both can be used to shuttle ions between two electrodes to store and release electrical energy. At first sight, replacing lithium with sodium in a rechargeable battery might therefore seem straightforward.

There are good reasons to try. Sodium is widely available and sodium-ion batteries can rely on electrode materials containing abundant elements such as iron and manganese. But chemical similarity does not mean electrochemical equivalence. A sodium ion is larger and heavier than a lithium ion, and its interaction with the materials surrounding it is different. As a consequence, replacing Li⁺ with Na⁺ changes much more than the identity of the charge carrier.

The electrodes have to accommodate a different ion. Their structures may respond differently as sodium is inserted and removed. The electrolyte has to transport and solvate it. New interfaces form between the electrolyte and the electrodes. Even graphite, the standard anode material of most commercial lithium-ion batteries, does not store sodium under conventional conditions nearly as effectively as it stores lithium ¹.

A sodium-ion battery is therefore not simply a lithium-ion battery containing a different element. Understanding why requires looking at what happens to sodium once it enters the battery.

Graphite does not play by the same rules

Charging a conventional lithium-ion battery involves moving lithium ions from the positive electrode through the electrolyte and storing them in the negative electrode. Graphite is particularly good at this job. Its carbon atoms are arranged in sheets, and lithium can reversibly occupy the spaces between them, a process known as intercalation. It would be convenient if sodium behaved in the same way. It largely does not.

The poor ability of conventional graphite to accommodate sodium has long been one of the reasons why lithium-ion concepts cannot simply be transferred to sodium-ion batteries. Instead, one of the most widely studied negative-electrode materials is hard carbon ².

Hard carbon is still carbon, but structurally it is very different from graphite. Rather than a regular stack of extended carbon sheets, it contains disordered graphitic domains, defects and pores. This disordered architecture provides environments in which sodium can be stored, but it also makes the underlying mechanism considerably harder to describe.

Where exactly does the sodium go? Researchers have proposed contributions from adsorption at defects and surfaces, insertion between graphitic layers and storage associated with nanopores. The relative importance of these mechanisms depends on the structure and microstructure of the carbon. This is more than a microscopic detail: where and how sodium is stored determines the voltage profile, reversible capacity, first-cycle losses and, ultimately, the energy that a complete cell can deliver.

Researchers at CIC energiGUNE and collaborators have studied this connection between charge-storage mechanisms, carbon structure and electrochemical performance ³. Their analysis highlights an important point: maximizing the amount of sodium that an anode can store is not enough. The potential at which that storage occurs and the irreversible losses during the first cycle are equally important when the material is incorporated into a full battery.

The problem is therefore not simply to find a carbon that accommodates more sodium. It is to understand how its structure stores sodium and then engineer that structure so that capacity, voltage and efficiency improve together. This has led researchers to explore different ways of controlling hard-carbon structure, including the use of lignocellulosic biomass as a precursor. Work has shown that even apparently simple processing decisions, such as acid treatment of the biomass precursor, can affect the resulting carbon and its behaviour as a sodium-ion anode ⁴.

And the negative electrode is only half of the problem. At the positive electrode, sodium ions have to repeatedly leave and re-enter a solid structure. Layered transition-metal oxides are attractive candidates because sodium can be reversibly extracted from and inserted into spaces between layers of metal and oxygen atoms. Compositions based on relatively abundant elements such as iron and manganese are particularly interesting ⁵.

Again, however, accommodating sodium is not enough. The host structure has to survive the process. A useful example is the layered oxide P2-Na₂/₃[Fe₁/₂Mn₁/₂]O₂, investigated by researchers from CIC energiGUNE and collaborators ⁶. The material can provide high capacity, but its long-term stability strongly depends on the voltage range over which it is operated.

This produces a familiar battery dilemma. Increasing the operating voltage can increase the amount of energy extracted from a material. But pushing the electrode further can also trigger structural transformations that make subsequent cycles less reversible.

The researchers compared cells operating in different voltage windows and combined electrochemical measurements with structural characterization and theoretical calculations. Above approximately 4.0 V versus Na+/Na, the cathode undergoes a high-voltage phase transition. Avoiding this transition improves capacity retention, revealing a direct connection between the structural state of the electrode and its long-term electrochemical behaviour.

Changing the chemical composition can also alter this structural response. In another study, researchers investigated the effect of introducing titanium into sodium manganese-rich layered oxides ⁷. A certain degree of Ti substitution helped the crystal structure accommodate electrochemically induced strain. Too little was insufficient to stabilize it, while further substitution introduced other destabilizing effects.

Other studies have approached the same problem from a different angle, examining how the precise stoichiometry of P2 layered oxides affects their performance ⁸, or following their structural evolution under different current rates and dopants using operando techniques ⁹. The lesson is that there is no single property called “a good sodium cathode”. Composition, atomic arrangement, voltage and cycling conditions are interconnected. Even an element that does not directly provide the stored charge can determine how well the electrode survives sodium repeatedly moving through its structure.

A different chemistry

Layered oxides are not the only possible positive electrodes. Sodium chemistry allows other structural families to be explored.

One particularly instructive example is NaFePO₄, the sodium analogue of the well-known lithium iron phosphate chemistry. Researchers involving CIC energiGUNE have used in situ X-ray diffraction to follow how NaFePO₄ changes during sodium insertion and extraction ¹⁰. They have also shown that the reaction mechanism itself depends on how rapidly the electrode is charged or discharged ¹¹.

This is a subtle but important point. We often describe an electrode material as if it had a fixed reaction mechanism. In practice, what happens inside it can depend on how the battery is operated. Computational work has gone further by investigating sodium diffusion in NaₓFePO₄ ¹². Combining experiments and modelling in this way makes it possible to connect what is observed at the battery level with the motion of ions through an atomic structure.

But even understanding both electrodes is not enough. Between them lies the electrolyte, and the sodium ion spends much of its journey there. It becomes surrounded by solvent molecules, travels across the cell and eventually reaches an electrode surface. At that interface the electrolyte can decompose, producing a solid-electrolyte interphase, or SEI.

This apparently thin layer can have a disproportionate influence on battery behaviour. Researchers at CIC energiGUNE have investigated both the composition and evolution of the SEI in sodium-ion electrodes ¹³ and, more broadly, the relationship between electrode-electrolyte interphases, transport properties and electrochemical performance in non-aqueous sodium-ion batteries ¹⁴.

The interface illustrates particularly well why changing lithium for sodium is not a simple substitution. The chemistry of the ion influences its solvation, its transport and the decomposition reactions that occur when it reaches an electrode. A material that can reversibly store sodium may still perform poorly if the interface around it continuously consumes electrolyte or sodium during cycling.

This is why sodium-ion research has to consider the cell as a system. Graphite may have to give way to hard carbon. Positive electrodes require structures able to tolerate repeated sodium insertion and extraction. Electrolytes and additives have to create suitable transport conditions and stable interfaces.

And every attempt to solve one of these problems can affect the others.

Sodium is not the new lithium

Lithium has a fundamental advantage that materials engineering cannot simply remove: it is the lightest metal and has a very low electrochemical potential. Sodium is heavier and its electrochemical potential is less favourable, placing intrinsic constraints on the gravimetric energy density that sodium-ion batteries can reach.

That does not necessarily make sodium a worse battery chemistry. Energy density is only one parameter of an electrochemical storage system. Cost, raw-material availability, lifetime, power, safety and operating temperature can become equally important depending on the application. A battery designed for a mobile phone, an electric vehicle or stationary storage does not necessarily have to optimize the same variables. And sodium chemistry itself offers several possible ways of balancing them.

CIC energiGUNE researchers have explored, for example, low-cost phosphate-based cathodes for aqueous sodium-ion batteries ¹⁵, Prussian Blue compounds as positive electrodes in aqueous systems ¹⁶, alternative sodium layered oxides [5,8,9], hard-carbon anodes [2,3,4] and even materials such as NaTiOPO₄ designed to modify or potentially avoid some of the interfacial problems normally associated with sodium-ion anodes ¹⁷.

These are not different routes towards exactly the same battery. They represent different ways of deciding which compromises are acceptable.

This changes the original question. The relevant challenge may not be how to make sodium behave as much like lithium as possible. Research on hard carbons shows that sodium may require a different type of host structure. Work on layered oxides shows that extracting more energy from an electrode can alter its structure and compromise its stability. Studies of NaFePO₄ show that the reaction pathway itself can depend on cycling conditions. And research on interfaces shows that storing sodium reversibly is only part of the problem: the chemistry taking place around the active material matters as well.

Sodium-ion batteries are therefore not lithium-ion batteries in which one element has simply been exchanged for another. Changing the ion changes the materials that host it, the structures they adopt, the reactions they undergo and the interfaces they form.

Sodium may not need to beat lithium at its own game. The more interesting question is whether understanding its different chemistry will allow us to play a different one.

 

The BRTA is a consortium that remains a step ahead of future socio-economic challenges worldwide and in the Basque Autonomous Community; it addresses them through research and technological development, thus projecting itself internationally. The BRTA centres collaborate to generate knowledge and transfer it to Basque society and industry so as to make them more innovative and competitive. The BRTA is an alliance of 17 R&D centres and cooperative research centres with the support of the Basque Government, the SPRI and the Chartered Provincial Councils of Araba, Bizkaia and Gipuzkoa.

 

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Scientists have discovered a class of metal that can unexpectedly resist extreme cold using an unusual mechanism. Normally such temperatures would make similar materials brittle and vulnerable to breaking. The findings point to new principles for designing materials for cryogenic environments.

An international team led by University of California, Berkeley, Lawrence Berkeley National Laboratory and the University of Oxford has uncovered ¹ a novel microscopic mechanism that allows two metal alloys to remain remarkably damage-tolerant at just 20 kelvin, or -253°C.

Most metals become stronger when they are cooled, but some pay a price. The class of metals called body-centred cubic metals (such as iron, tungsten and chromium) have a particular atomic structure which can make them increasingly brittle as temperatures fall. At extremely low temperatures, a crack that might normally be absorbed by the metal bending or deforming can instead cause it to fracture.

The new study discovered that two experimental niobium-titanium-based alloys can avoid this problem even at just 20 kelvin, or -253°C. The metals remained remarkably resistant to cracking, with no measurable transition to brittle behaviour at the lowest temperature tested. The researchers found that this is due to the alloys effectively switching how they deform as they enter the deep freeze.

Normally, bending and deformation of body-centred cubic metals relies heavily on the movement of line-like defects in their crystal structure known as dislocations. At low temperatures, these become increasingly difficult to move, restricting the material’s ability to deform around a crack and making a fracture more likely.

In the alloys studied, however, a different process takes over. The researchers observed nanoscale ‘twinning’, in which small regions of the crystal reorganise into mirror-image orientations, coupled with a local transformation of the crystal structure. When these newly formed structures reach the boundaries between neighbouring crystals, they create concentrated points of stress that trigger new defects in the metal. These defects then allow the material to keep deforming rather than cracking.

The process is a little like a road network responding to frozen, blocked roads by opening new routes. As the conventional routes for deformation become increasingly difficult to use, the formation of twins creates new sites from which the defects needed for deformation can emerge. This helps the metal to absorb the forces building up around a crack, rather than breaking.

The discovery could provide scientists with a new strategy for designing metals capable of operating in exceptionally cold environments, including for energy, transport and aerospace sectors.

To find out how the alloys behaved in such extreme cold, the researchers used the Engin-X instrument at the ISIS Neutron and Muon Source in Oxfordshire. They cooled samples to around -253°C using gaseous helium. They then exposed the samples to a beam of neutrons while a testing machine pulled them from either end, precisely measuring how much force they could withstand and how far they stretched before breaking.

The team then used powerful electron microscopes to examine the tested metal at extremely small scales, allowing them to see the tiny structural changes that had taken place around cracks and inside the material. They also used atom-probe analysis to map the distribution of individual elements, alongside computer modelling to understand how the different mechanisms worked together to prevent brittle failure.

The study involved researchers from the University of California, Berkeley; Lawrence Berkeley National Laboratory; the University of Oxford; the University of Bristol; the ISIS Neutron and Muon Source, Science and Technology Facilities Council; the University of California, Irvine; Pacific Northwest National Laboratory; Texas A&M University; and Nanyang Technological University in Singapore.

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Once upon a time, in a world very far from ours, there were a group of scientists devoted to the study of bacteria, or prokaryotes, who called themselves ‘biologists’, and a different group of researchers, who studied eukaryote organisms, and who received the name of ‘organismologists’. Organismologists were very proud of the obvious differences between their discipline and that of the biologists, and flagged those differences every time they needed to show that organismology was a science wholly independent of biology, completely ‘irreducible’ to it, and who demanded a totally different set of concepts, principles, and research methods, far more significant than the more or less trivial similarities between both disciplines and their objects. After all, this was a matter of common sense: for example, the concept of an ‘organ’ or ‘digestive system’, or the principles of sexual reproduction, do not apply to bacteria save in a very metaphoric sense; indivual organisms of the same species (for example, siblings) have usually great and important differences between them to an extent that bacteria of the same type have not; and also most multicellular organisms, contrarily to prokaryotes, can often be observed and manipulated without the need of very sophisticated instruments. Organismologists accepted, as a matter of course, that eukaryote organisms had evolved millions of years ago from bacteria, that both types of beings shared a common biochemistry and genetics (though much more complex in the case of eukaryotes), and that both types of beings engaged in lots of mutual relations, so strongly that, in general, bacteria are fundamental for the life of eukaryotes, either as prey, as parasites, or as symbionts. But all this was not relevant enough to turn into ashes the obvious truth that the systems in which multicellular organisms (and even unicellular eukaryotes) consisted were so complex and radically different from the simplicity of bacteria, as to deserve a completely independent field for their systematic study. ‘We would not understand anything important about organisms’, leading organismologits used to proclaim, ‘if we were forced to describe them as mere aggregates of individual bacteria… what very probably they are, of course’.

I think that nearly everybody that knows something about biology in our own world would easily realised that organismologists were right in some sense (eukaryotes, and particularly multicellular organisms, are terribly more complex than bacteria, and ‘irreducible’ to these in many ways), but wrong in other sense (their fields of study are not really that ‘heterogeneous’). I shall argue in this series that the situation of social scientists resisting the ‘naturalisation’ of their disciplines is similar to the resistance of organismologists to be considered as just a ‘branch’ of a deeper and more general discipline called ‘biology’: they are right in pointing to the significant differences between ‘social systems’ and ‘(simpler?) living systems’, but these differences do not ground the conclusion that social science is not a ‘natural’ science. I will also try to argue, however, that, due to some features of social systems, the undavoidable ‘naturalistic nature’ of social sciences gives little comfort to those optimists who might have thought that social sciences could turn ‘more scientific’ by recognising their own naturalness. So, my conclusion will be something like acknowledging that, it is not that  social sciences ‘should’ be naturalised, but that they are ‘natural sciences’ as they are, but that they probably cannot become significantly more ‘successful’ in an empirical or theoretical sense as they are now.

Naturalism (see, e.g., Ross 2011) is usually seen by many social scientists and philosophers of the social sciences as a frightening menace, and often as a completely wrong and misguided approach. It is usually amalgamated with other philosophical monsters, such as positivism or reductionism, and at times even with ‘realism’ or ‘rationalism’ (forming with them a very poisonous combination often referred to as ‘scientism’). I will discuss in this series the often proclaimed conflict of social, or human, sciences with naturalism, reductionism and positivism, and why I think that social scientists should not worry at all at any of these three supposed Behemoths. Let’s start with positivism. So many horrible things have been said about positivism, that now it passes as a matter of fact that one should not be a positivist; particularly, the story is often told that those sciences, both natural, social or hermeneutic, that tried to rigidly follow the precepts of positivism, ended in something similar to a ‘brain death’ state, with nothing interesting to discover about their realm of study. For many of these critics, as well as for some visionary scientists that tried to apply those precepts, ‘positivism’ seemed to be reducible to the boring inductivist strategy of collecting as many single data one can, and then finding out by mere statistical recounting all the ‘regularities’ those data might happen to exhibit. Of course, no real science actually works in this naively Baconian way, nor most self proclaimed (and much less those merely referred to by others as) ‘positivist’ philosophers, have defended such a caricaturesque idea of the scientific method. But even when a more liberal and benevolent description of the positivist admonitions is adopted, most people in the social sciences still reject that positivism is a sensible methodological approach. Just to take an example of this criticism, consider a paper by Isaac Reed (2010). Reed starts by making a distinction between the ‘context of investigation’ (i.e., what the social scientist does) and the ‘context of explanation’ (i.e., what the social scientist is trying to explain, the object she studies). According to Reed, the basic mistake of what he calls ‘positivism’ is the normative relation that is assumed to exist between both contexts:

 

Positivism begins with a reduction of the context of investigation to the rules of logic and to a precise language whose meanings are transparent to those in the scientific community who use it. It also proposes that the context of explanation be reduced to that which can be observed—and, to a great degree, that which can be measured. Then, through the process of inductive generalization, covering laws are imported from the context of explanation to the context of investigation. (Reed, 2010, 24; bold font words are original’s italics).

 

Besides the fact that it seems to be inconsistent to assert that “positivism reduces the context of investigation to the rules of logic and to a precise language” just a few lines after having asserted that “the context of investigation would include both of Reichenbach’s contexts (of discovery and justification)” (my italics), for positivists’ ‘context of discovery’ was explicitly taken as not reducible to logical rules, Reed’s explanation is rather obscure about what the ‘importation’ from one context to the other would consists of. Perhaps this simply means that the regularities that are observed in the ‘context of explanation’ are ‘accepted’ or at least ‘proposed’ in scientific papers or books (but, if it is so, what’s wrong with it?). And Reed makes a caricature of the process of ‘importation’ by reducing it to ‘inductive generalization’, overlooking the essential role of hypotheses and theories, as well as of abductive and analogical methods (that only in the most extreme and unrealistic views of science of some positivist philosophers were considered as illegitimate, if at all). The consideration of hypotheses also allows to see that it is an oversimplification to assert that in the context of explanation only ‘what can be observed’ counts: if by ‘observation’ it is understood exclusively what is observable ‘by the naked eye’, then the assumption is false about how science, even social science, works (for all ‘observation’ is ‘theory laden’, and most data are extremely sophisticated entities; consider, for example, empirical data inflation rates); if, instead, ‘observation’ is taken to mean ‘anything that is intersubjectively detectable by some means’, then one does not see what’s wrong in taking into account only ‘observable’ things in what you want to scientifically describe and explain: is Reed suggesting that social scientists must assert things about which there is absolutely no way to empirically determine whether they are as we are asserting? I doubt it.

 

 

References

Reed, I., 2010, “Epistemology Contextualized: Social Scientific Knowledge in a Post-Positivist Era.” Sociological Theory. 28, 61-80.

Ross, D., 2011, “Naturalism: the place of society in nature”, in Jarvie, I., and J. Zamora Bonilla (eds.), The SAGE Handbook of Philosophy of Social Sciences, London, Sage, 121-136.

 

 

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In 2004, physicists isolated graphene, a sheet of carbon just one atom thick. It launched the study of two-dimensional (2D) materials: crystals a few atoms thick in which electrons are confined to a plane and can behave quite differently from those in ordinary solids. The family of known and predicted 2D crystals has since grown to thousands of members. Two recent studies show how computation can search that family for the most promising ones, the first for unusual electronic “topology”, the second for crystals well suited to twisting.

A hidden property of electrons

Electrons in a crystal can only have energies within allowed ranges called bands, separated by forbidden gaps. If a gap separates the filled electrons from the empty states, the material is an insulator. In a semimetal, filled and empty bands just touch, so a few electrons can move freely.

Two insulators can still differ at a deeper level, described by topology: a property of the whole set of electron states that cannot change smoothly, only by closing the gap or breaking a protecting symmetry. A doughnut and a coffee mug are topologically alike because each has one hole, and neither can become a sphere without tearing.

The idea took off with the quantum spin Hall effect. Proposed for graphene in 2005, it proved unobservable there because the effect is far too weak. A 2006 proposal for thin layers of mercury telluride was confirmed in 2007. In such a topological insulator the interior blocks current, yet the edges conduct, with electrons of opposite spin travelling in opposite directions, which protects them against many kinds of imperfection.

Symmetry-based methods known as topological quantum chemistry in 2017 made it possible to decide whether a computed electronic structure is topological. Applied to three-dimensional crystals, they pointed to thousands of candidates. Flat crystals lagged behind, with only about 400 known topological or related monolayers.

The first study, “Two-dimensional Topological Quantum Chemistry and Catalog of Topological Materials” ¹, adapts these methods to 2D crystals and applies them to 8,872 entries in two computational databases. It finds 4,073 with nontrivial topology or a related property called obstruction, including 905 topological insulators, 2,129 topological semimetals and 1,003 obstructed atomic insulators, plus 36 close variants. In an obstructed insulator the electrons are centred on empty positions between the atoms rather than on the atoms themselves. The bulk looks ordinary, but cutting the crystal along certain lines produces edge states, and small flakes can carry fractions of an electron’s charge at their corners. The study also calculates edge states for selected materials. Its catalogue includes over 100 monolayers already made in laboratories, but most entries are computer predictions whose properties remain to be tested.

Twisting layers

Stack two atomic sheets and rotate one slightly, and the mismatch creates a large interference pattern, called a moiré pattern, much like two overlapping window screens. Electrons feel this longer repeating pattern, and under the right conditions their bands become nearly flat. Electrons in a flat band have little energy of motion, so their mutual repulsion dominates and strongly correlated behaviour can emerge.

In 2011, calculations predicted that two graphene sheets twisted by about 1.1 degrees, a “magic angle”, would have such flat bands. In 2018, experiments at that angle revealed insulating states caused by electron repulsion, and superconductivity. Twisted layers of other materials, such as MoTe₂ and WSe₂, have since shown many correlated phases, though the mechanisms are still debated.

Most work has focused on these few materials, because most crystals have electronic structures too complicated to predict once twisted. The second study, “2D theoretically twistable material database” ², therefore defines a material as theoretically twistable if its low-energy electrons admit a simple description. In a metal, the relevant electrons must sit at isolated points, as in graphene. In an insulator, the top of the filled band or the bottom of the empty band must stand clear of other bands. Insulators must also have gaps between 0.2 and 3 electronvolts, because larger gaps make electrical contacts difficult. The search was limited to crystals with at most 12 atoms in the repeating cell and four chemical elements.

Starting from the first study’s database, it identifies 61 semimetals and 1,568 insulators. It ranks them with a score and sorts them by lattice shape (about half are hexagonal), by where in momentum space the relevant electrons sit, and by the strength of spin-orbit coupling, the link between an electron’s spin and its motion. These choices shape the moiré pattern, which can resemble honeycomb, kagome or square lattices. Square-lattice moiré systems have been proposed but not yet realized, and could help simulate models relevant to cuprate superconductors.

Calculations on twisted bilayers of SnSe₂, SnS₂, ZrS₂, HfS₂ and Sc₂CCl₂ at a twist of about 7 degrees show isolated flat bands, as the database predicts. Experiments connect the theory to the laboratory. Bulk crystals of SnSe₂, SnS₂, HfS₂, GaTe and ZrNCl were grown. Single layers of several candidates, including SnSe₂, HfSe₂, ZrS₂ and WS₂, were peeled off with a gold-assisted technique that yields larger, cleaner flakes. A dual-gated two-layer SnSe₂ device was built for electrical measurements, and a twisted two-layer HfS₂ device was used for scanning tunnelling measurements near absolute zero.

The direction is clear. Instead of discovering materials by trial and error, it is becoming possible to search systematically for crystals with chosen properties, then test them layer by layer.

 

Author: César Tomé López is a science writer and the editor of Mapping Ignorance

Disclaimer: Parts of this article may have been copied verbatim or almost verbatim from the referenced research paper/s.

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About the author: José Luis Granados Mateo is a former secondary-school and sixth-form STEM teacher, having taught physics, chemistry and mathematics. He is currently a postdoctoral researcher in the epistemology of science at the University of the Basque Country (UPV/EHU). 

 

When I taught physics, chemistry and mathematics to secondary-school and sixth-form students, a correct answer was sometimes where the interesting part began. I would ask why they had used a particular equation. A solution that had looked perfectly sound could become much less convincing; occasionally the reverse happened, and a student whose algebra had gone wrong could explain the physics rather well. Nothing on the page had changed. My estimate of what the student understood had.

I have been thinking about those exchanges while reading the research on generative AI in education. Students can now submit a convincing explanation, solve a numerical problem or produce working code with considerable help from a language model. It is easy to see the achievement and much harder to work out what the student has learnt along the way.

That difficulty cannot be settled by appealing to the virtues of an unaided mind. Scientific work depends on instruments, notation, diagrams, software and other people. Delegating part of a calculation may be entirely sensible. Yet teaching has a complication that is easy to overlook from the perspective of an expert: the operation being delegated may be one of the things through which a beginner is meant to acquire expertise.

An experiment by Hamsa Bastani and colleagues brings this problem into unusually sharp focus.¹ Nearly a thousand pupils at a secondary school in Turkey took part in a study comparing two GPT-4 systems with a control condition without AI. GPT Base offered assistance resembling a general-purpose chatbot. GPT Tutor had additional material from teachers, including solutions and common mistakes, and instructions to guide pupils with hints rather than give away the answer.

During practice, both systems helped. The estimated scores were 48% higher than the control mean with GPT Base and 127% higher with GPT Tutor. These are relative differences, not percentage-point gains. On the tests that followed, however, the pupils had to work without assistance. The GPT Base group then scored an estimated 17% below the control mean. GPT Tutor largely mitigated that penalty, but its users showed no statistically significant advantage over the control group. The tests took place within the study sessions, so they tell us about immediate independent performance rather than retention months later.

Had the researchers stopped at the practice exercises, they would have had an encouraging result for both systems. They did not stop there, and the educational interpretation changed. A pupil working with AI had become more successful at the task. Whether that success belonged to the pupil in any lasting sense was another matter.

Psychologists have long distinguished performance during acquisition from learning: a relatively durable change in knowledge or skill. Soderstrom and Bjork review the evidence for that distinction, including cases in which fluent practice leads to disappointing retention and others in which slower, more error-prone practice produces better results later.² Watching someone learn, we inevitably see performance. To find out what remains, we need to look again after a delay, withdraw some of the support or ask for an application in a different context. Even then, what we have is evidence to interpret, not a direct view of understanding.

In STEM, much of the important work happens before the calculation. A mechanics problem requires a choice of system, a judgement about the relevant interactions and some representation of the situation. Chemistry involves moving between observable phenomena, molecular accounts and symbols on a page. A program that runs is the endpoint of decisions about what to separate, what to abstract and how to test it. Nersessian’s work on model-based reasoning gives representations a central place in scientific thought: constructing and revising a model can be part of arriving at an explanation, rather than merely a way of presenting one.³

A language model can help at almost any of these points. Perhaps the student has made the difficult modelling decisions and wants an algebraic check. Perhaps the model has chosen the principle, drawn up the representation, done the algebra and supplied an explanation before the student has formed a view of the problem. A questionnaire asking whether both students “used AI” would record the same answer.

There is an obvious temptation here to defend struggle. I am wary of it. Spending half an hour looking for a formula can be frustrating without being especially instructive, and a teacher who withholds every useful clue has not necessarily protected the student’s learning.

Worked examples offer a familiar counterexample. A novice studying a solution can attend to the structure of a procedure without having to search blindly for it. Barbieri and colleagues’ meta-analysis, covering 43 articles, 55 studies and 181 effect sizes, found a medium benefit for mathematics performance (g = 0.48).⁴ Removing some work can help a learner do other work more productively. The judgement lies in deciding what to remove.

Nor will the right decision remain right indefinitely. In a 2025 meta-analysis of the expertise reversal effect, Tetzlaff and colleagues brought together 60 experiments involving 5,924 participants and 176 effect sizes. Learners with little prior knowledge benefited from greater instructional assistance (d = 0.505); for those with high prior knowledge, lower-assistance conditions were preferable (d = −0.428).⁵ These are heterogeneous results across educational contexts, not estimates specifically for generative AI. Still, they help explain a familiar experience: an explanation that once made a procedure possible can later get in the way of carrying it out.

This is part of what Koedinger and colleagues call the assistance dilemma: when should instruction provide information, and when should it require the learner to generate it?⁶ With a conversational model, the practical difficulty is that help need never run out. Another prompt can produce another hint, or an answer, or a complete solution to a problem the student has scarcely begun to consider.

Pablo Rodríguez Sánchez raised a related question in Mapping Ignorance, in Why teach calculus in the age of AI. Software can compute many standard derivatives and integrals almost immediately, and AI interfaces make such tools easier to consult. That does change the case for teaching manual procedures. It does not dispose of it. Working through integration by parts can make its relation to the product rule visible; substitution can bring the chain rule into focus from the other direction. Some of the value of a procedure lies in the relationships a student encounters while carrying it out. Requiring the procedure without regard to those relationships would miss the point just as thoroughly as abandoning it because a machine is faster.

We already move parts of our thinking into the world. We write a number down so that we do not have to remember it, or set a reminder for something we expect to forget. Risko and Gilbert describe such actions as cognitive offloading: changing the processing demands of a task through physical action and external resources.⁷ Its consequences are worth studying, but the fact that someone has offloaded a task is not in itself evidence of cognitive decline.

For history and philosophy of science (HPS), this should be familiar ground. Giere and Moffatt describe scientific cognition as distributed across people and artefacts.⁸ On this account, instruments, representations and social arrangements can be parts of the system through which scientific knowledge is produced. A physicist who uses a computer to integrate a differential equation has not thereby revealed a failure to understand physics.

She does, though, need some grounds for trusting the result. She must know what calculation is appropriate, which assumptions it involves and when the output ought to make her suspicious. A beginner may still be acquiring those resources. If every mechanics problem arrives already represented and ready for calculation, there may be very little occasion to learn how to represent one.

“Which formula do I use?” was a question I heard often. Usually, in the cases I remember, the difficulty was not simply a forgotten equation. The student had not yet made sense of the situation in a way that gave any equation a purpose. Supplying the formula could rescue the exercise while leaving that difficulty untouched. A question about the forces, or about what was being treated as the system, could sometimes help much more.

The records from Bastani’s experiment are suggestive in this respect. GPT Base users more often requested answers, and the authors interpreted their interaction and error analyses as consistent with copying solutions. GPT Tutor elicited more attempted answers and requests for help. The surveys, administered at the end of the sessions, revealed a further complication. GPT Base users did not perceive the disadvantage visible in their unassisted scores; GPT Tutor users rated their performance more favourably even though no significant exam advantage had been detected.¹ Students’ impressions were not a dependable guide to what the assistance had done for them.

But the evidence does not all point towards disappointment. In an introductory physics course at Harvard, Kestin and colleagues compared a purpose-built AI tutor with an established active-learning class.⁹ Their randomised crossover study covered two lessons, with students experiencing both conditions. The tutor incorporated scaffolding, targeted feedback and self-pacing. Median post-test scores were 4.5 in the AI condition and 3.5 in the classroom condition. Measured against the pooled pre-test median, the gain in the AI condition was more than twice as large. Seventy per cent of students spent less than the 60 minutes allocated to classroom learning on the AI activity; the median was 49 minutes. They also reported greater engagement and motivation.

That is an interesting result on its own terms. It concerns particular content, a carefully prepared tutor and tests taken after the lessons. The intervention also combined several differences, including the setting, pace and prerecorded introductions, so the study cannot tell us how much of the benefit came from the language model alone. Nor does it establish long-term retention. Within those limits, it is good reason to take the design of AI-supported instruction seriously. Efficiency and learning need not be enemies.

Programming provides a less reassuring case. Bassner and colleagues reported a three-arm randomised trial at the Technical University of Munich, with 275 introductory programming students in the reported sample.¹⁰ During a 90-minute exercise, students used either the scaffolded tutor Iris, unrestricted ChatGPT or conventional web resources without AI. Both AI groups achieved higher scores on automated tests of their code and reported less frustration. Neither showed a statistically significant advantage in knowledge gains or code comprehension. Only Iris showed an increase in intrinsic motivation. There was clearer evidence of better task performance than of better understanding, although the absence of a significant learning difference does not establish that the groups learnt exactly the same amount.

Three studies cannot carry a general theory of AI in education. Their students, tasks and measurements are too different, and their time horizons too short. What they do make difficult to ignore is the need to decide whose competence an assessment is measuring. If a tool remains available throughout, successful performance may tell us a great deal about the person–tool combination and rather less about a change in the person.

The larger reviews do not make this much easier. Boolzen and colleagues’ 2026 review identified 85 eligible controlled studies of cognitive outcomes in STEM; 49 studies, yielding 59 effect sizes, entered the meta-analysis.¹¹ A conventional random-effects model gave a positive mean effect, alongside extraordinary heterogeneity (I² = 96.32%). Its prediction interval ran from g = −1.52 to g = 3.20. For comparable settings, the model therefore allows for effects extending from substantial harm to substantial benefit. It would be a mistake to read the positive average as a reliable forecast for a new classroom intervention.

The authors also found funnel-plot asymmetry, consistent with possible publication bias. Using a robust Bayesian adjustment, they obtained an overall estimate close to zero (μ = 0.076), with substantial uncertainty. The heterogeneity remained. Asymmetry need not be caused by publication bias, and the adjusted estimate depends on modelling assumptions; it is not a final answer about whether AI helps students learn.

Their moderator analysis is more helpful for thinking about instruction. They coded the learning outcome and the change in students’ activity relative to the control condition. The patterns favoured augmentation over substitution, but these were comparisons across studies, not randomised tests of those design choices. Much variation remained unexplained, and no combination of the examined moderators reliably supplied a sufficient condition for a large effect.¹¹ The distinction is promising as a research question. We do not yet have a rule for applying it to every lesson.

Wu and colleagues’ 2026 meta-analysis sounds more optimistic: 35 studies, 4,193 participants and a positive mean effect of g = 0.670, with a 95% confidence interval of 0.495–0.844.¹² The two reviews are not estimating quite the same thing. Wu’s synthesis ranges across disciplines and includes motivation, engagement and self-efficacy alongside cognitive outcomes. It also reports very high heterogeneity (I² = 91.444%). Its tests did not detect publication bias, which is different from establishing its absence. Most included studies concerned higher education.

I would hesitate to choose between those reviews on the strength of their averages. An answer-giving chatbot, a tutor that asks for explanations and a debugging assistant may use closely related models while organising the student’s activity very differently. Asking for “the effect of ChatGPT on learning” begins to sound like asking for the effect of books. We would immediately want to know which books, who was reading them and what they were being asked to do.

Meanwhile, students are getting on with using the tools. PISA 2025 cannot resolve the causal questions raised by the experiments, but it gives some sense of their scale. On average across OECD countries, 46% of 15-year-olds reported using AI chatbots at least weekly to help them learn. In Spain, the figure was 54%. The Spanish percentages reported for preliminary research, summarising assigned texts and drafting written work were 42%, 40% and 33%, respectively. Only 8% reported never or almost never using AI for any of the schoolwork purposes examined.^13,14

The achievement patterns deserve attention, though they are easily overread. After adjustment for students’ socioeconomic profile, the OECD-average results generally favoured non-users over those reporting AI use for specific tasks such as drafting or summarising. Weekly use for the broader purpose of helping with learning was associated with roughly similar science performance to non-use. For some specific tasks, moderate users did better than very frequent users.¹³

A pupil who is struggling may seek more help. Schools may encourage AI use in response to difficulties that already exist. And frequency tells us very little about the encounter itself: requesting an answer, interrogating a hint and challenging an explanation can all count as using a chatbot. Those possibilities are not findings that explain away PISA’s associations; they are reasons why the associations cannot establish what AI caused.

PISA also examines opportunities to evaluate AI-generated information at school. Some descriptive patterns look favourable, but the overall positive association with that activity is not observed, on average, after adjustment for students’ and schools’ socioeconomic profiles.¹³ The report gives us no simple causal claim about the benefits of teaching students to check AI output.

There is nevertheless an educational question here that deserves more than a slogan. Mapping Ignorance has discussed it in Critical thinking for the unstoppable use of artificial intelligence. In STEM, asking a student to check an answer presupposes that something is available with which to check it. Does the student know what order of magnitude to expect? Which assumption matters? What evidence would bear on the explanation? A fluent paragraph can be physically impossible, but fluency alone will not tell a beginner where it goes wrong.

It is also worth keeping the chronology straight. Generative AI cannot be the sole explanation for declines in educational achievement that began before ChatGPT was publicly available. What PISA establishes more usefully here is that the practices under discussion are already part of ordinary schoolwork. Teachers have to make decisions while the evidence is still developing.

Some of those decisions will be quite small. A worked solution may be exactly what a pupil needs on Monday. A few weeks later, providing the whole solution may remove an opportunity to reconstruct the method. AI could make it easier to vary the support: ask for a representation before proposing an equation, invite a prediction before showing a simulation, or offer a flawed argument for the student to diagnose. These are plausible uses, not capabilities we should assume a system can deliver reliably simply because it holds a convincing conversation.

Assessment poses a related problem. Students will need to work competently with tools, as scientists and engineers do, and that competence deserves to be assessed. But if we also want to know whether they can perform a particular operation themselves, there must be an occasion when the tool is not doing it for them. We have to say what belongs in the learner’s own repertoire, and then find an assessment that gives us reasonable evidence of it.

For someone working in History and Philosophy of Science, the interest extends beyond the ownership of a correct answer. Scientific competence involves judgement about models, evidence, instruments and the reach of a procedure. A student may know a formula and still not know when it applies. An experienced scientist may quite reasonably delegate its numerical solution while retaining responsibility for the assumptions and interpretation. Learning to make those distinctions is part of becoming competent.

That brings me back to the classroom question. When I asked why a student had used an equation, I wanted access to the reasoning behind the calculation. With generative AI, the visible work may belong to a temporary partnership, and locating that reasoning becomes harder. The partnership itself need not be objectionable. What matters educationally is what repeated participation in it does to the student.

Over time, can the learner represent a problem more confidently, choose a method, recognise an implausible result or decide when help is needed? If so, the tool may be contributing to the acquisition of expertise. If those capacities scarcely change while the submitted answers become more polished, the same outward success has a different meaning.

I do not think the most useful question is whether students should use AI in STEM. It is what they should still be learning to do, how the assistance bears on that learning, and when it ought to recede. A correct answer was never a guarantee of understanding. We now have to be more deliberate about finding out what lies behind it.

 

 

 

References

1. Bastani, H., Bastani, O., Sungu, A., Ge, H., Kabakcı, Ö. & Mariman, R. (2025). ‘Generative AI without guardrails can harm learning: Evidence from high school mathematics’. Proceedings of the National Academy of Sciences, 122(26), e2422633122. 10.1073/pnas.2422633122
2. Soderstrom, N. C. & Bjork, R. A. (2015). ‘Learning versus performance: An integrative review’. Perspectives on Psychological Science, 10(2), 176–199. 10.1177/1745691615569000
3. Nersessian, N. J. (2002). ‘The cognitive basis of model-based reasoning in science’. In P. Carruthers, S. Stich & M. Siegal (eds), The Cognitive Basis of Science, pp. 133–153. Cambridge University Press. 10.1017/CBO9780511613517.008
4. Barbieri, C. A., Miller-Cotto, D., Clerjuste, S. N. & Chawla, K. (2023). ‘A meta-analysis of the worked examples effect on mathematics performance’. Educational Psychology Review, 35, Article 11. 10.1007/s10648-023-09745-1
5. Tetzlaff, L., Simonsmeier, B., Peters, T. & Brod, G. (2025). ‘A cornerstone of adaptivity – A meta-analysis of the expertise reversal effect’. Learning and Instruction, 98, 102142. 10.1016/j.learninstruc.2025.102142
6. Koedinger, K. R., Pavlik, P. I. Jr., McLaren, B. M. & Aleven, V. (2008). ‘Is it better to give than to receive? The assistance dilemma as a fundamental unsolved problem in the cognitive science of learning and instruction’. In B. C. Love, K. McRae & V. M. Sloutsky (eds), Proceedings of the 30th Annual Conference of the Cognitive Science Society, pp. 2155–2160. Full text
7. Risko, E. F. & Gilbert, S. J. (2016). ‘Cognitive offloading’. Trends in Cognitive Sciences, 20(9), 676–688. 10.1016/j.tics.2016.07.002
8. Giere, R. N. & Moffatt, B. (2003). ‘Distributed cognition: Where the cognitive and the social merge’. Social Studies of Science, 33(2), 301–310. 10.1177/03063127030332017
9. Kestin, G., Miller, K., Klales, A., Milbourne, T. & Ponti, G. (2025). ‘AI tutoring outperforms in-class active learning: An RCT introducing a novel research-based design in an authentic educational setting’. Scientific Reports, 15, 17458. 10.1038/s41598-025-97652-6
10. Bassner, P., Lenk-Ostendorf, B., Beinstingel, R., Wasner, T. & Krusche, S. (2026). ‘Less stress, better scores, same learning: The dissociation of performance and learning in AI-supported programming education’. Computers and Education: Artificial Intelligence, 10, 100537. 10.1016/j.caeai.2025.100537
11. Boolzen, C., Kuhn, J., Flegr, S., Rott, E.-M., Stausberg, N. & Küchemann, S. (2026). ‘Evidence of impact and interpretational limits of generative AI in STEM education: a systematic review and meta-analysis on cognitive learning outcomes’. Artificial Intelligence Review. Advance online publication. 10.1007/s10462-026-11665-9
12. Wu, X., Zhu, P., Zhang, J., Yin, M. & Wang, Y. (2026). ‘ChatGPT’s impact on student learning outcomes: a meta-analysis of 35 experimental studies’. Humanities and Social Sciences Communications, 13, 684. 10.1057/s41599-026-07019-z
13. OECD (2026). PISA 2025 Results (Volume I): Future-Ready Students. Paris: OECD Publishing. 10.1787/73451bc5-en
14. OECD (2026). PISA 2025 Results (Volume I): Spain. Country note. OECD. Country note

 

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Author: José R. Pineda got his Ph.D. from University of Barcelona in 2006. Since 2007 he has worked for Institut Curie and The French Alternative Energies and Atomic Energy Commission. Currently he is a researcher of the EHU. He investigates the role of stem cells in physiologic and pathologic conditions.

 

One of the ideas most of us learn early in biology is that only a few specialized cells can communicate through electrical signals. Neurons do it. Muscle cells do it. Epithelial cells, the cells that form our skin and line most organs, supposedly do not. However, a recent study by Yu and Granick demonstrates that this picture may not be entirely correct. In fact, these seemingly ordinary cells appear capable of generating electrical spikes of their own when tissue integrity is disturbed. Despite  epithelial cells have traditionally been viewed as passive structures whose main functions are to form protective barriers, absorb nutrients, and maintain tissue integrity, Yu and Granick challenges this long-standing idea in a striking way. Their work demonstrates that epithelial cells can generate electrical spikes resembling action potentials, revealing a previously unrecognized form of bioelectrical communication that may help coordinate tissue responses after injury ¹.

The finding is surprising because epithelia are among the most abundant tissues in the body. They line the skin, digestive tract, airways, and many internal organs. Although these tissues are known to participate in wound healing and cellular communication, they were not believed to possess the kind of rapid electrical activity usually associated with the nervous system. The new study suggests that this assumption may have been incomplete. Under certain conditions, epithelial cells appear capable of producing coordinated electrical signals that spread across remarkably large distances. To investigate this phenomenon, the researchers employed two different epithelial models: the first model consisted of primary human skin keratinocytes (the major cellular component of the epidermis). The second model used Madin-Darby Canine Kidney (MDCK) cells (a classical epithelial cell line frequently employed in cell biology research). Both cell types were grown until they formed dense, confluent monolayers resembling miniature sheets of epithelial tissue.

The key experimental tool was a multielectrode array, often abbreviated as “MEA”. This technology can be imagined as a highly sensitive electronic “listening device” containing dozens of microscopic electrodes embedded in a culture surface. When cells generate electrical activity, even extremely small voltage fluctuations can be detected simultaneously at multiple positions. Multielectrode arrays are routinely used to study neurons, but their application to epithelial tissues is relatively uncommon. After establishing epithelial monolayers on these arrays, the researchers created a small and highly localized injury using a focused laser beam. The laser produced controlled damage in a tiny region at the center of the culture while leaving surrounding cells intact. This experimental design allowed the team to observe how cells located at various distances reacted to the injury. Electrical signals were then monitored continuously for one hour. What they observed was unexpected: within the epithelial sheets, electrical spikes appeared shortly after injury and persisted for more than sixty minutes!! These spikes displayed a characteristic sequence of depolarization, repolarization, and hyperpolarization, terms commonly used to describe action potentials in neurons. However, there was one major difference, while neuronal action potentials last a few milliseconds, the epithelial spikes unfolded over one to two seconds, making them roughly one thousand times slower. Despite their slower kinetics, the electrical signals were surprisingly robust, measurements showed that spikes could be detected as far as 740 micrometers from the injury site, a distance corresponding to dozens of cell diameters (Figure 1). Even more remarkably, their amplitude did not progressively decrease with distance as one would expect from a simple wave spreading outward from a central source. In some cases, signals recorded farther away were as large as, or even larger than, those detected closer to the wound. This observation suggested that distant epithelial cells were not merely receiving a weakened signal from injured neighbors. Instead, they may have been generating their own electrical responses as part of a collective tissue-wide process.

 

Discovering the spikes was only part of the story. The obvious next question was what actually produced them. Were epithelial cells using the same electrical machinery found in neurons, or was something entirely different at work? To answer this, the researchers began dissecting the molecular mechanisms one by one. They began by testing the role of calcium (one of the most important intracellular messengers in biology). Calcium ions regulate a wide range of cellular activities, including contraction, migration, secretion, and gene expression. To determine whether calcium was necessary for epithelial spiking, the researchers added EDTA (a molecule that binds calcium and reduces its availability). Surprisingly, once calcium availability was reduced, the electrical activity virtually vanished!! This immediately suggested that calcium was not just associated with the phenomenon but was an essential part of it. Next, the team examined the contribution of cellular mechanics, because it is known that epithelial cells continuously generate mechanical forces through interactions between actin filaments and myosin motor proteins, a system known as “the actomyosin network”. This machinery allows cells to contract, change shape, and exert forces on neighboring cells. To disrupt this process, the researchers treated cultures with blebbistatin (a selective inhibitor of myosin II activity). Once again, electrical spiking was largely abolished. The similarity between the effects of calcium depletion and myosin inhibition suggested that electrical activity was intimately linked to the mechanical state of the tissue. This observation raised an intriguing possibility: perhaps epithelial electrical signaling is not driven by voltage-gated ion channels (as in neurons), but instead by channels that respond to mechanical forces. To test this hypothesis, the investigators focused on mechanosensitive ion channels, specialized proteins embedded within cell membranes that open when cells are stretched, compressed, or subjected to mechanical stress. Using the inhibitor GsMTx4 (which blocks several mechanosensitive channels including Piezo1), the researchers observed a partial reduction in electrical activity. While spiking was not completely eliminated, both amplitude and coordination decreased substantially. This result implicated mechanosensitive channels as key components of the signaling pathway. To really prove their implication, next the researchers activated them directly using specific pharmacological compounds. One molecule, GSK1016790A, activates the TRPV4 channel. Another, Yoda-1, specifically activates Piezo1. Remarkably, activating these channels was sufficient to generate large electrical spikes even in the absence of any injury. In other words, simply stimulating mechanosensitive channels could reproduce the electrical behavior observed after tissue damage. This provided strong evidence that mechanical sensing lies at the heart of epithelial electrical excitability.

 

Based on their findings, the authors proposed a positive feedback mechanism: 1) mechanical stress activates mechanosensitive ion channels, allowing calcium to enter the cells. 2) rising calcium levels stimulate actomyosin contraction, generating additional mechanical stress. 3) this new stress then activates more mechanosensitive channels, sustaining the cycle. Such a feedback loop could explain why spiking persists for long periods and why cells distant from the wound remain electrically active. One particularly interesting aspect of the study is its potential relevance to wound healing. Successful tissue repair requires large numbers of cells to coordinate their behavior across considerable distances. Cells must migrate, proliferate, and remodel tissue structures in a synchronized manner. Traditional explanations have emphasized biochemical signaling molecules and calcium waves. The electrical spikes described here introduce an additional layer of communication that may operate on intermediate spatial and temporal scales. According to the authors, these signals could complement chemical and mechanical communication systems, helping tissues organize collective responses after injury. However, the researchers are careful to acknowledge the study’s limitations. Their experiments were performed in cultured epithelial monolayers rather than living organisms. Although the results clearly demonstrate intrinsic electrical excitability in epithelial cells, it remains unknown whether the same phenomenon occurs in intact tissues during natural wound healing. Furthermore, the exact relationship between these electrical spikes and cellular behavior has not yet been determined. It is still unclear whether the spikes actively drive tissue repair or simply accompany mechanical disruption. Additional work involving animal models, voltage-sensitive imaging, and targeted genetic manipulation of mechanosensitive channels will be required to answer these questions.

 

In conclusion, the study by Yu and Granick reminds us that biology still contains unexpected surprises, even in tissues that have been studied for decades. A simple layer of epithelial cells, once considered electrically silent, may in fact possess its own form of excitability. Rather than transmitting information through millisecond action potentials like neurons, epithelial tissues appear to communicate through slower, mechanically driven electrical spikes capable of coordinating activity across hundreds of micrometers. Whether these signals prove to be a central component of tissue physiology remains to be seen. What is already clear, however, is that the electrical life of cells extends far beyond the nervous system!!

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Authors: Mary M. Hausfeld, Assistant Professor in Management, University of Limerick and Jochen Menges, Director of the Center for Leadership in the Future of Work, University of Zurich

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Galaxies rotate faster than the matter we can see should allow. Evidence for an unseen, gravitating substance began to build in the 1930s with Fritz Zwicky’s studies of galaxy clusters, and strengthened in the 1970s as Vera Rubin measured how stars orbit within spiral galaxies. Nearly a century later, dark matter is still known almost entirely through its gravity. It holds galaxies together and shaped the web of cosmic structure, yet its nature remains unknown.

Axions, plural

One candidate has an unusual origin. In the late 1970s, physicists proposed a new particle to solve a puzzle in the theory of the strong nuclear force. Frank Wilczek named it the axion, after a laundry detergent, because it promised to clean up the problem. By 1983 theorists had shown that axions about a millionth of an electronvolt in mass could make up cold dark matter, the slow-moving kind. Later, string theory, an attempt to unify gravity with quantum physics, suggested that nature may contain not one axion but many, with masses spread across a vast range. Some of these particles could be extraordinarily light: around 10⁻²² electronvolts, more than 10²⁷ times lighter than an electron.

Such lightness has a striking consequence. The quantum wavelength of a particle grows as its mass shrinks, and for these axions it stretches to astronomical size, comparable to the roughly half-kiloparsec cores of small dwarf galaxies, about 1,600 light-years. Dark matter would then behave less like a swarm of tiny grains and more like a vast wave, often called wave or fuzzy dark matter. Simulations from 2014 showed that every galaxy halo would have a dense central core with a flat density profile, surrounded by a shimmering pattern of interfering waves. The flat core contrasts with the steep central spike predicted by the simplest cold dark matter models. The same wave nature also prevents very small clumps from forming, which may help explain why fewer small satellite galaxies are seen around our Galaxy than those models predict.

There is, however, a serious difficulty. Light from distant quasars passes through clouds of hydrogen that imprint absorption lines on it, the Lyman-alpha forest, which records how matter was clumped on small scales in the early Universe. If a single ultralight species made up all dark matter, these data demand a considerably larger mass. One influential analysis set a lower limit of about 2×10⁻²⁰ electronvolts, some two hundred times heavier than the favoured value. Separately, deep surveys show no clear drop in the number of faint galaxies, which argues against single axions lighter than about 2.5×10⁻²² electronvolts. Both conclusions assume one kind of axion.

A new analysis ¹ asks what changes if dark matter is a mixture. On large scales, it finds, all species feel the same gravitational field, so they respond together and behave much like one effective axion. The mass of that stand-in depends on each species’ mass and on its share of the total dark matter, with lighter species weighing more heavily. The recipe was tested against a detailed calculation for two species, 30% at 10⁻²² electronvolts and 70% at five times that mass. It reproduced the overall suppression of structure well, missing only some fine oscillations, and the resulting difference in predicted mass fluctuations was below 0.1%. If this holds, a multi-axion universe could build large-scale structure much like a single-axion one, with the cut-off in faint galaxies set by the effective mass. The method extends to any number of species and could seed future simulations.

Inside galaxies the picture changes. On these smaller scales the species act independently, and each weaves its own interference pattern with its own grain size. Projected along the line of sight, these produce density fluctuations of only a few percent, yet they bend light enough to blur the lines of greatest magnification in a gravitational lens, called critical curves, into corrugated bands.

The Dragon test

The Dragon Arc offers a test. This is a spiral galaxy, seen when the Universe was half its present age, stretched and magnified by the galaxy cluster Abell 370. In 2025, observations with the James Webb Space Telescope revealed more than forty individual stars in it, each appearing as a brief flicker when magnified by intervening stars in the cluster. Their positions scatter broadly around the critical curve, and an earlier analysis found this matches wave interference. Cold dark matter clumps would instead confine them to a narrower band skewed in the opposite direction. Reading the scatter as a wavelength of about ten parsecs gives a lensing effective mass of roughly 2.4×10⁻²² electronvolts, assuming about 2.4×10¹⁴ solar masses lie inside the critical curve. This differs from the large-scale effective mass, because lensing depends on each species’ share of the projected density. It is not a detection of axions but a model-dependent interpretation. If the two species suggested by dwarf galaxies, about 1.9×10⁻²² and 2.3×10⁻²¹ electronvolts, made up the halo, the lighter would supply roughly 89% of the projected density near the arc.

The most distinctive prediction concerns position. Heavier axions are expected to gather near the centre of a halo and lighter ones to dominate farther out, so the lensing effective mass should change from place to place. A single species cannot do this. The Cosmic Horseshoe, a lensed galaxy where the telescope may find around sixty flickering stars per pointing, could test it by comparing two positions about five arcseconds apart. A mismatch would hint at several species.

This work shows how a mixture of ultralight particles could look like a single one across the cosmos while revealing its true complexity inside galaxies, perhaps reconciling cosmic constraints with galactic evidence. Proving it will require better simulations, more realistic models of multi-species haloes, and further lensing observations.

 

Author: César Tomé López is a science writer and the editor of Mapping Ignorance

Disclaimer: Parts of this article may have been copied verbatim or almost verbatim from the referenced research paper/s.

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Authors: Eider Fernandez & Igor Baroja-Careaga, Esneki Zentroa (Leartiker S.COOP)

 

Probiotics are part of a rapidly expanding field of research. They are live microorganisms that, when administered in adequate amounts, may confer health benefits[1]. Among the most extensively studied probiotics, some species of Lactobacillus and Bifidobacterium have been associated with the maintenance of gut microbiota balance and with several physiological functions[2]. Producing these microorganisms usually requires nutrient-rich culture media. But what if such bacteria could be obtained from a food by-product nowadays regarded as waste? This question formed the starting point of a study carried out by Esneki Dairy Centre – Leartiker to assess the potential of cheese whey as a substrate for producing microbial biomass enriched in microorganisms with probiotic potential.

The challenge of cheese whey

Cheesemaking inevitably generates substantial amounts of whey: a yellowish liquid released from the curd that still carries lactose, soluble proteins, minerals and other valuable compounds. In fact, whey can represent around 85% of the original milk volume used in cheese production[3].

Despite this nutritional richness, whey remains a difficult stream to manage for many artisanal dairies. This is particularly true in the Basque Country, where many cheesemaking farms are small, family-run businesses located in rural areas[4]. Its highly perishable nature means that whey must be preserved or processed soon after production, making storage, collection and transport especially challenging when volumes are small and geographically dispersed.

Moreover, uncontrolled whey discharge results in a high organic load that can affect aquatic ecosystems. Paradoxically, the same nutrients that make cheese whey a potential pollutant are also what give it considerable biotechnological value.

A natural culture medium

From a microbiological standpoint, cheese whey is not merely a residual stream, but a naturally nutrient-rich matrix[5]. Its lactose content, together with soluble proteins, minerals and other available compounds, provides a favourable environment for the growth of lactic acid bacteria, widely used microorganisms in fermented foods and increasingly explored for their probiotic potential.

The working hypothesis was simple: by steering whey fermentation under controlled conditions, it could be possible to recover a biomass enriched in microorganisms of interest, while at the same time increasing the stability and value of the by-product itself.

To explore this possibility, several fermentation strategies were tested using whey generated during the production of blue cheese from pasteurised cow’s milk. The study compared three different approaches:

• Fermentation of previously pasteurised whey (Protocol 1).
• Fermentation of whey after a deproteinisation step (Protocol 2).
• Direct fermentation of raw whey, without any prior treatment (Protocol 3).

Two different blends of commercial microorganisms, inspired by the naturally diverse microbial communities found in kefir, were also evaluated. These included; Choozit Kefir DV LYO 1000L (Danisco) (starter culture A) and Ferlac Kefir Type C (Abiasa) (starter culture B). Additionally, unfermented whey (that is, whey to which no starter cultures were added and which was not subjected to fermentation) from each protocol was analysed as a control sample. Controlled fermentation processes were carried out under monitored conditions. Throughout the fermentation, key parameters were monitored, including temperature (25 ± 1 °C), incubation time (16 ± 1 h for starter culture A and 21 ± 1 h for starter culture B) and pH evolution, with fermentation being considered complete once the pH fell below 4,6. These measurements allowed the identification of the conditions that most effectively supported the growth and enrichment of the target microbial populations.

 

Exploring the microbiome through metagenomics

However, assessing the success of a fermentation process requires more than simply determining how many microorganisms grow. It is also essential to identify which species are present and how the microbial community changes over time.

Traditional culture-based microbiological methods remain fundamental tools for quantifying and isolating viable microorganisms. Yet they have important limitations when complex microbial communities need to be characterised, as they only detect microorganisms able to grow under the selected culture conditions. As a result, part of the microbial diversity present in the sample may remain undetected. To obtain a more comprehensive view of the microbial community, the study incorporated high-throughput amplicon sequencing, an approach that enables the direct analysis of DNA present in a sample and the identification of microorganisms regardless of their ability to grow under laboratory conditions.

Bacterial communities were characterised by amplifying the V4 region of the 16S rRNA gene, one of the most widely used markers in bacterial diversity studies. Fungal and yeast communities were analysed through the ITS region — the Internal Transcribed Spacer — which is considered the standard marker for fungal diversity studies.

Sequencing was performed using Illumina technology, generating approximately 100,000 reads per sample for bacteria and around 40,000 reads for fungi and yeasts. These sequences were then compared against specialised databases to determine the identity of the microorganisms present and estimate their relative abundance.

Before interpreting the results, sequencing depth was assessed using rarefaction curves. These curves showed a clear trend towards saturation, indicating that most of the microbial diversity present in the samples had been adequately captured.

Which protocol worked best?

High-throughput amplicon sequencing revealed clear differences among the fermentation strategies tested.

Fermentations carried out using raw whey (Protocol 3) maintained a more diverse bacterial community than those in which the whey had first been subjected to thermal treatment (Protocol 1 and Protocol 2), as can be seen in Figure 1, as can be seen in Figure 1, the number of observed microbial taxa increases with sequencing depth. This suggests that the partial preservation of the native microbiota originating from the cheesemaking process may play an important role in shaping the fermentation outcome.

 

 

 

In contrast, the diversity of moulds and yeasts decreased. This trend may be related to the origin of the whey, which was obtained from blue cheese production, where specific mould (Penicillium roquefoti) species are deliberately enriched during manufacture. The competitive advantage of these dominant fungi appears to favour the development of a more specialised microbial community, reducing the abundance and diversity of other microbial populations present in the whey (Figure 2).

 

 

Principal coordinates analysis (PCoA) based on Jaccard distances (Figure 3) showed a clear separation among the different fermentation protocols, indicating that each strategy gave rise to distinct microbial communities. In parallel, the relative abundance of profiles (Figure 4) made it possible to visualise how particular species increased or decreased depending on the conditions applied.

 

 

 

 

Amplicon sequencing also enabled the identification of the dominant microorganisms during the process. In most samples, Lactococcus lactis was particularly abundant. This result was expected, as this bacterium was included in the commercial starts cultures used and is widely employed in dairy fermentations. However, some fermentation conditions, particularly those involving starter culture B, also favoured the development of species such as Lacticaseibacillus rhamnosus and Bifidobacterium animalis, wich were also present in the commercial starter culture. These microorganisms are frequently associated with probiotic applications[6]^,[7]^,[8].

To identify the most suitable protocol for producing a fermented whey enriched in microorganisms with probiotic potential, both microbial abundance (including aerobic mesophilic bacteria, yeasts and moulds) and the diversity of the resulting microbial communities were evaluated. The highest microbial counts were obtained in whey samples produced using Protocol 3, which was based on raw whey, and fermented with starter culture B. (Average counts of 8.2 log CFU/mL were obtained with starter culture A, and average counts of 8.5 log CFU/mL with starter culture B).

Furthermore, as mentioned previously, the highest levels of microbial diversity were observed in the samples produced using Protocol 3, where fermentation was carried out directly on raw whey without prior heat treatment.

 

Overall, the results pointed to the most effective strategy also being the simplest from a technological perspective: the direct fermentation of raw whey, without prior thermal treatment using starter culture B. This approach maintained high microbial diversity while reducing energy requirements and simplifying the overall process.

An opportunity for the circular economy

Beyond the microbiological results, the broader relevance of this work lies in showing that the role of whey within the cheesemaking chain can be reconsidered.

Rather than being treated as a waste stream associated with management costs, whey can be viewed as a raw material capable of supporting valuable biotechnological processes. Controlled fermentation not only helps stabilise whey but also makes it possible to harness the nutrients it still contains to generate added-value microbial biomass.

Such strategies are closely aligned with the principles of the circular bioeconomy, in which by-products are no longer seen as the end of a production chain, but as the starting point for another. In a context where sustainability and efficient resource use are increasingly important, initiatives of this kind show how microbiology and omics technologies can help turn an environmental challenge into an opportunity for innovation.

 

The PRO2O project (grant agreement No. 00003-BIO2022-48) was funded through the 2022 Bioeconomy Innovation Projects funding programme of the Basque Government’s Department of Economic Development, Sustainability and Environment.

References

[1] Guarner F, Requena T, Marcos A. Consensus statements from the Workshop “Probiotics and Health: Scientific evidence”. Nutr Hosp. 2010 Sep-Oct;25(5):700-4. PMID: 21336423.

[2] Martin, A. J. M., Serebrinsky-Duek, K., Riquelme, E., Saa, P., & Garrido, D. (2023). Microbial interactions and the homeostasis of the gut microbiome: the role of Bifidobacterium. Microbiome Research Reports, 2. https://doi.org/10.20517/mrr.2023.10

[3] González Siso, M. I. (1996). The biotechnological utilization of cheese whey: A review. Bioresource Technology, 57(1), 1–11. https://doi.org/10.1016/0960-8524(96)00036-3

[4] Esneki Zentroa – Leartiker (2022). “El sector quesero en Euskadi 2021”. Available at: El-sector-quesero-en-Euskadi.pdf

[5] Figueroa Pires, A., garcía Marnotes, N., Díaz Rubio, O., Cobos García, A., Dias Pereira, C. (2021). Dairy by-products: A review on the valorization of whey and second cheese whey. Foods, 10: 1067

[6]Neethu, M., Bunt, C., Hussain, M., 2015. Comparison of Microbiological and Probiotic Characteristics of Lactobacilli Isolates from Daity FOod Products and Animal Rumen Contens Microorganims 3, 198-212.

[7] Rama, G.R., Kuhn, D., Beux, S., aciel, M.J., Volken de Souz, C.F., 2019. Potential apllications of dairy why for the production of lactic acid bacteira cultures. Int Dairy J.

[8] Rodriguez-Palacios, 1., Staemplfli, H.R., Duffield, T., Weese, J.S., 009. Isolation of bovine intestinal Lactobacillus plantarum and Pediococcus acidilactici with inhibitory activity against Escherichia coli O157 and F5. J. Appl. Mcrobiol. 106, 393-401

 

The BRTA is a consortium that remains a step ahead of future socio-economic challenges worldwide and in the Basque Autonomous Community; it addresses them through research and technological development, thus projecting itself internationally. The BRTA centres collaborate to generate knowledge and transfer it to Basque society and industry so as to make them more innovative and competitive. The BRTA is an alliance of 17 R&D centres and cooperative research centres with the support of the Basque Government, the SPRI and the Chartered Provincial Councils of Araba, Bizkaia and Gipuzkoa.

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Author: Deven Desai, Professor of Business Law and Ethics; Associate Director for Law, Policy, and Ethics at the Machine Learning Center, Georgia Institute of Technology

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Scientists have developed remarkably long, precisely patterned molecular threads that could open new possibilities for designing advanced materials. The scientists also discovered these threads — called supramolecular polymers — can dramatically enhance brain cell activity. ¹

Built from self-assembling molecules, the longest threads reach dimensions greater than the diameter of a cell. By molecular standards, they are giant — roughly 100 times more massive than even very large conventional polymers and the largest known proteins in biology. Yet despite their enormous size, scientists can precisely control their lengths and organize them into chemically distinct segments with defined dimensions carrying opposite electrical charges.

That precision also produced an unexpected biological effect. In cell culture studies, the structures enhanced the growth and organization of neurons and increased synapse formation.

The findings introduce a new way to use self-assembly to build highly controlled supramolecular materials with precise physical arrangement of chemical structures. Ultimately, the work could inform materials’ design for a range of applications, including biomaterials for regenerative medicine.

“These structures represent a breakthrough in materials design, and we already discovered one useful application: their superbioactivity toward neurons, which will bring new opportunities in regenerative medicine,” said Northwestern’s Samuel I. Stupp, who led the study. “Typically, when we design a regenerative material, we add biological signals, designed to activate cell receptors. Here, the material itself becomes highly bioactive simply through the precise organization of electrical charges and its dynamic behavior. That introduces a very different way of thinking about how materials can communicate with cells.”

Bringing precision to self-assembly

The new study builds on Stupp’s long history working with supramolecular materials, dynamic structures that form when molecules spontaneously organize through weak, reversible interactions. While conventional polymers, like plastics, hold together using strong, permanent chemical bonds, supramolecular polymers are dynamic, allowing their components to move and reconfigure, which generates life-like properties in synthetic systems. Supramolecular polymers exist in all living organisms, where they perform essential functions and hold promise for future soft matter technologies.

That flexible, dynamic nature can be useful for interacting with living cells in biomedical applications, but it also makes the structures difficult to control. Scientists can design the individual molecular building blocks but then struggle to control how long the resulting structures grow and how they organize their chemical components.

Stupp’s team overcame that limitation by using novel designs of molecules and carefully controlling their assembly process. With this strategy, the researchers could dictate the threads’ lengths and keep them uniform. Once the growth stopped, the structures maintained their precise lengths rather than fusing together or rearranging.

“We let these filaments sit in a test tube for months, and they surprisingly didn’t change,” Stupp said. “They remained the same length and retained their segmented structures.”

Grow, stop, grow again

Stupp and his team traced that unusual ability to a previously unknown process his laboratory calls “self-capping supramolecular polymerization.” As a thread grows, flexible portions at the ends remain highly dynamic and, at proper temperatures, allow new molecules to join in a synchronized manner. Once the available building blocks are consumed, those flexible portions fold over and protect the ends. This effectively shuts down further growth by preventing threads from fusing together or undergoing “Ostwald Ripening,” a process in which smaller structures disappear while larger ones grow.

“To make them longer and longer, we just kept adding new molecules,” Stupp said. “The new molecules stick with strong noncovalent bonds to the growing thread and elongate the assembly, which led to a breakthrough in terms of size control.

“The collective molar mass of their noncovalently bonded monomers reaches billions of daltons, and thus they are ‘giga-assemblies.’ These are the largest supramolecular polymers ever made with this degree of precision. Once the monomer is fully consumed, they finish growing and their dimensions remain stable.”

Approximately the size of one proton or neutron, a dalton is a tiny unit that scientists use to measure the mass of molecules and atoms. More than a billion daltons is enormous by molecular standards. For comparison, the largest common polymers of plastics have molar masses in the range of 10 million daltons, and the largest proteins in nature reach approximately 3 to 5 million daltons.

Researchers can later restart growth by supplying more building blocks. By adding different types of molecules in sequence, the researchers can create precisely defined segments with different chemical properties. In the study, Stupp and his team created threads with positively and negatively charged segments. Because opposites attract, the researchers expected the threads to clump together. Instead, they remained stable in water because the “capping” mechanism prevented the assemblies from fusing together.

Small anchor, big difference

To explore how the pattern of electrical charges might interact with living cells, Stupp and his team turned to neurons, which carry a strong negative charge. The team exposed several threads with different designs to cellular cultures containing cortical neurons.

“The first thing we did was make a structure with only positively charged segments, and it basically killed the neurons,” Stupp said. “Then, we tried a structure with only negatively charged segments, and nothing happened because the neurons repelled the materials.”

When Stupp’s team used supramolecular assemblies with randomly mixed positive and negative charges, the neurons didn’t respond in a notable way. But then the team designed a thread with the breakthrough polymerization strategy comprising a small positively charged segment sandwiched between two negatively charged segments of different lengths. Something interesting and unexpected occurred.

The small positive region anchored the thread to the negatively charged surface of a neuron. Repelled by the neuron’s negative charge, the thread’s negative segments remained highly mobile and in constant motion since they could not escape.

“When we used only positively charged segments, they suffocated the neuron and killed it,” Stupp said. “But with only one positively charged segment surrounded by negative ones, it couldn’t do that anymore. And the negative segments, which ordinarily couldn’t get near the neuron, were forced to stay near it because they were anchored.”

Neurons grow and spring to life

Neurons treated with the precisely segmented threads grew longer neurites — the long projections neurons use to communicate with other cells. The treated neurons also formed more elaborate branches, gaining the ability to connect with neighboring cells.

“The neurons matured to an amazing level,” Stupp said. “They grew long and highly branched neurites, which is how they can start making synaptic connections in the brain and in the spinal cord.”

After just seven days, treated neurons were much more active than untreated neurons. When stimulated, treated neurons produced a calcium response — a sign of neuronal activity. Their overall calcium activity was four times greater. And, after 14 days, treated neurons formed more synapses than untreated neurons.

Stupp and his team saw another striking effect in cultures of human neural progenitor cells, which are immature cells that can develop into neurons. Although these cultures typically grow in flat layers, the cells instead organized into raised, three-dimensional clusters connected by axons. This organization resembled aspects of the brain’s white and gray matter, where somas are separated from axons.

No signals required

Perhaps most surprisingly, the molecular threads produced these effects without carrying biological signals specifically designed to encourage neurons to grow. Stupp posits the negatively charged segments recruit specific proteins already present around the cells that help neurons survive, grow and communicate. These proteins, called neurotrophic factors, have positively charged domains. Stupp’s team also found laminin — an important protein that holds tissues together and has positively charged domains — accumulating along the supramolecular threads near neurons.

Stupp hypothesizes that the interplay between attraction and repulsion causes the threads’ negative segments to rapidly move toward and away from the neurons in a “tapping” motion. Proteins recruited by the negative segments may be drawn toward receptors on the neurons, while electrostatic forces push the segments away. This repeated tapping, occurring on millisecond timescales, could help enhance biological signaling. A live cell movie included in the Science paper has captured this phenomenon.

Beyond neurons, Stupp says the new polymerization strategy could eventually enable scientists to build long molecular structures containing many carefully positioned chemical segments. That could open opportunities to create new materials and devices with features that extend over very long distances.

“We discovered something we had never seen before in chemistry or in biology,” Stupp said. “This work gives us a new level of control over supramolecular materials. In the future, we can imagine creating many segments with different properties. The unknown functions of these structures are likely to be as surprising as the superbioactivity observed on neurons. We’re just beginning to imagine the possibilities.”

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In 1911, Heike Kamerlingh Onnes cooled mercury to a few degrees above absolute zero and watched its electrical resistance vanish. Lead soon joined the list of superconductors, losing its resistance below about 7.2 kelvin. A full explanation arrived in 1957: electrons bind into Cooper pairs that move together as one collective state below a critical temperature. Breaking a pair costs a minimum amount of energy, called the energy gap, so inside the gap a superconductor offers no states for single electrons.

Yu–Shiba–Rusinov states

Magnetism is an old enemy of this order. Magnetic impurities were known to suppress superconductivity, and in the 1960s Yu, Shiba and Rusinov showed theoretically that a magnetic atom disturbs the pairs around it and traps a localized state with an energy inside the gap. These Yu–Shiba–Rusinov (YSR) states were first seen atom by atom in 1997, using a scanning tunneling microscope (STM): a needle-sharp metal tip that measures the tiny current of electrons tunneling across a vacuum gap to a surface.

A different story concerns two superconductors joined by a very weak link. In 1962, Brian Josephson predicted that Cooper pairs can tunnel through such a link with no voltage at all, an effect confirmed in 1963. When a voltage is applied, another process takes over: multiple Andreev reflection. An electron whose energy lies inside the gap cannot enter a superconductor alone. Instead it is sent back as a hole, the absence of an electron, while a Cooper pair slips in, as Andreev described in 1964. Between two superconductors under a voltage V, a particle can bounce back and forth, gaining energy eV with each crossing, until it can finally escape above the gap. When n crossings are needed, the conductance shows a peak at a voltage equal to the sum of the two gaps divided by n. This pattern, explained in the early 1980s, is called subharmonic gap structure. For lead on lead the sum is 2.7 millivolts, so peaks are expected near 2.7, 1.35 and 0.9 millivolts.

Impurity states and Andreev reflections have usually been treated as separate subjects. A recent experiment ¹ places them in the same device. A nickelocene molecule, a nickel atom sandwiched between two five-carbon rings, sits on a lead surface above a single iron atom trapped between the molecule and the lead. On its own, the molecule carries a spin that appears as characteristic steps in the measured spectra. Above the iron, those steps vanish and YSR states appear instead. Density-functional calculations explain why: the magnetic moments of molecule and iron point in opposite directions and almost cancel, leaving a leftover spin of one half on the iron. That spin couples to the lead and produces a single pair of YSR states.

The second superconductor is a lead-coated STM tip, lowered toward the molecule at 2.4 kelvin. Far away, electrons tunnel through a wide vacuum barrier and the tip merely reads out the YSR states, which appear as lopsided peaks near the edge of the gap. As the tip approaches, the junction becomes more transparent, meaning electrons cross it more easily, and the setup becomes a weak link between two superconductors. At moderate conductance, new peaks appear at half the sum of the gaps, the signature of second-order Andreev reflection. At the highest conductances, a sharp peak develops at zero voltage: the Josephson contribution. Thermal fluctuations of the superconducting phase broaden this peak, as is typical of STM junctions.

These stages do not simply stack. As the tip approaches, the YSR peak moves to lower energy and mingles with the Andreev peaks. The interpretation is that the bound state becomes a stopping point along the Andreev path. Peaks then appear at the tip’s gap plus the bound-state energy, divided by n, rather than at the ordinary positions. This is called YSR-assisted multiple Andreev reflection.

Odd and even orders

A simple argument explains why odd and even orders differ. Each reflection carries the particle to the opposite electrode, and only the lead surface contains the magnetic atom; the tip has none. After an odd number of crossings the particle ends on the surface, where it can land in the bound state. The peak shifts and acquires the lopsided shape typical of tunneling into a single level. After an even number it ends in the tip, among ordinary states, and those peaks stay closer to their usual positions, although the second-order peak still turns lopsided at higher conductance as a YSR-assisted component splits off. Simulations reproduce this pattern. In the measurements, thermal broadening blurs finer details such as the third-order peak, and small features near zero voltage seem to reflect a mixture of both processes.

Reproducing the evolution of the spectra required two changes together: higher transparency and a stronger exchange coupling between the iron spin and the lead. Raising transparency alone gives a growth of the key peak that the measurements do not show. A likely reason is that the approaching tip slightly squeezes the molecule and strengthens the coupling, though this is an inference. The model treats the spin as classical and its two parameters as effective ones, so it is a phenomenological decomposition rather than a unique microscopic extraction. It also cannot capture the zero-voltage peak.

Even so, the result shows that YSR states and Andreev reflections are two limits of one problem, tuned continuously within a single molecular junction. Under suitable conditions, such spin-active links might also host a Josephson diode, in which supercurrent flows more easily in one direction, or a π-junction, in which the two superconductors prefer opposite phases. These remain possibilities, not demonstrated effects.

Author: César Tomé López is a science writer and the editor of Mapping Ignorance

Disclaimer: Parts of this article may have been copied verbatim or almost verbatim from the referenced research paper/s.

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