The central difficulty is that electromagnetic coupling in these low dimensional systems is not governed by any single mechanism. At the smallest scale, atomic layer spin-orbit coupling dictates how electron spins respond to electric fields. At the nanoscale, the In-Pb interfacial proximity effect allows superconducting and normal-state regions to borrow properties from one another across their shared boundary. At the mesoscale, the texture of grains and domains imprinted during fabrication shapes bulk anisotropy. And at the macroscale, hot pressing parameters such as temperature, pressure, and holding time determine which microstructural features actually survive into the finished component. Any predictive model that ignores one of these tiers risks producing numbers that look plausible but violate the fundamental physics.

Researchers led by a team reporting in Frontiers in Chemistry have now built a neural architecture specifically designed to respect this hierarchy. Their framework, called the Multiscale Cross Attention Electromagnetic Coupling Network, or MSCA-EMNet, embeds each of the four physical scales into independent, nonoverlapping channels of a hierarchical encoder. This design choice matters because it prevents the network from blurring together phenomena that operate at genuinely different length scales, a common failure mode when conventional deep learning models are applied to heterogeneous materials data.

The real innovation lies in how information flows between these channels. A bidirectional cross-scale attention module, dubbed BS-CrossAttn, places the query at scale k while drawing keys and values from the neighboring scales k plus or minus one. In practice, this means the network simultaneously performs upward aggregation, where fine-scale physics informs coarse-scale behavior, and downward constraint feedback, where macroscopic processing conditions discipline the interpretation of atomic-level features. Because both directions run in parallel, the model captures the mutual conditioning that real materials exhibit, rather than imposing a one-way causal chain that exists only in the mathematics of simpler architectures.

To connect the model to the messy reality of manufacturing, the researchers incorporated a Feature-wise Linear Modulation mechanism, known as FiLM, which maps hot pressing parameters and the applied magnetic field directly onto channel-level affine transformations. This gives the network a natural handle for inverse design: given a desired electromagnetic response, the model can identify the feasible windows of processing conditions most likely to produce it. A scale availability mask further allows training records with unequal coverage across the four scales to contribute meaningfully, using a learnable embedding that stands in for missing information rather than discarding valuable experimental data outright.

Physical consistency is enforced through a constraint that many machine learning approaches to materials science have historically overlooked. The nine-component electromagnetic coupling tensor, defined at a specified magnetic field and including three components of the interfacial magnetoelectric susceptibility, must satisfy Onsager reciprocity, the principle that direct and converse responses are symmetrically related in systems near equilibrium. By building this reciprocity requirement into the loss landscape, the researchers ensure that the network cannot produce magnetoelectric predictions that would violate thermodynamic constraints, no matter how well they fit the training data.

The empirical results are striking. Trained and validated on 1,200 samples drawn from density functional theory calculations and hot pressing experiments, MSCA-EMNet achieves an overall normalized mean absolute error of 0.041 and a coefficient of determination of 0.948. Compared against the strongest baseline model in the study, these figures represent improvements of 43 percent in error reduction and 7.2 percent in explanatory power. Perhaps more telling is the extrapolation degradation rate of 48.8 percent, which quantifies how gracefully the model’s accuracy declines when asked to predict outside the range of its training distribution, a scenario that routinely breaks conventional data-driven surrogates.

The reciprocity constraint pays dividends in a metric that speaks directly to physical plausibility. In baseline models, between 12 and 41 percent of predicted samples violated the Onsager relation, rendering them unusable for downstream device design regardless of their numerical accuracy. MSCA-EMNet reduces this violation rate to just 1.7 percent, a dramatic improvement that suggests the network has internalized the symmetry structure of electromagnetic coupling rather than merely memorizing input-output pairs. Cross-system transfer performance, measured between 0.86 and 0.89, further indicates that the learned representations generalize across different material configurations without requiring complete retraining.

To demonstrate practical utility, the researchers put the inverse design capability to the test. Starting from a target electromagnetic coupling tensor, the framework identified a feasible processing window of 168 to 174 degrees Celsius, 62 to 70 megapascals of pressure, 25 to 35 minutes of holding time, and a characteristic dimension of 8 to 12 micrometers. Six confirmatory experiments conducted within this window reproduced the target tensor within 7.6 percent on every component, closing the loop between computational prediction and physical realization in a way that few inverse design pipelines have achieved for multiscale electromagnetic materials.

The implications extend well beyond indium-lead heterostructures. As quantum devices, spintronic interconnects, and flexible electromagnetic materials push toward ever tighter integration of superconducting, magnetic, and mechanical functionalities, the need for predictive tools that honor physics while remaining flexible enough to learn from sparse experimental data will only intensify. By demonstrating that bidirectional cross-scale attention, physical reciprocity constraints, and inverse process design can be woven into a single coherent framework, this work offers a template that materials scientists across subfields are likely to adapt. The marriage of multiscale physics and modern machine learning, long promised and often overhyped, appears here in a form that delivers measurable, experimentally validated gains.

Subject of Research: Machine learning prediction of electromagnetic coupling in low dimensional In-Pb heterostructures fabricated by hot pressing

Article Title: A multiscale cross attention framework for predicting the electromagnetic coupling characteristics of low dimensional In-Pb heterostructures fabricated by hot pressing

Article References: Xi, Y., & Wang, L. (2026). A multiscale cross attention framework for predicting the electromagnetic coupling characteristics of low dimensional In-Pb heterostructures fabricated by hot pressing. Frontiers in Chemistry, 14, Article 1974299. https://doi.org/10.3389/fchem.2026.1974299

Image Credits: AI Generated

DOI: 10.3389/fchem.2026.1974299

Keywords: MSCA-EMNet, In-Pb heterostructures, hot pressing, electromagnetic coupling, cross attention, spin-orbit coupling, magnetoelectric susceptibility, Onsager reciprocity, inverse design, superconducting quantum devices, spintronics, density functional theory

The team, led by Muhammad Amir Khan of Qurtuba University of Science and Information Technology in Peshawar with colleagues in Pakistan, Korea and Malaysia, performed the calculations with the WIEN2k code using the full-potential linearized augmented plane-wave method within the GGA-PBEsol framework. Because praseodymium carries strongly localized 4f electrons, the researchers added a Hubbard U correction, with an effective on-site parameter of 6.0 electron volts and an exchange parameter of 0.7 electron volts, to capture the correlations that ordinary functionals miss. Structural optimization produced an equilibrium lattice constant of 8.60 angstroms, within 0.1 percent of the experimental value of 8.611 angstroms, a level of agreement that lends credibility to everything built on top of it. The ground-state energy at equilibrium was approximately minus 6324.7 rydbergs, and the smooth, parabolic energy-volume curve indicated a stable configuration that deforms harmonically under small pressures.

Mechanical testing followed from the same framework. The three independent elastic constants of a cubic crystal came out as C₁₁ equal to 160 gigapascals, C₁₂ equal to 95 gigapascals and C₄₄ equal to 55 gigapascals, satisfying the Born stability criteria for a cubic solid. From these, the Voigt-Reuss-Hill averaging scheme yielded a bulk modulus of 116 gigapascals, a shear modulus of 52 gigapascals and a Young’s modulus of 130 gigapascals. Pugh’s ratio, the bulk-to-shear modulus, came to 2.23, comfortably above the 1.75 threshold that separates ductile from brittle behavior, and Poisson’s ratio of 0.29 reinforced the picture of a metallic, workable solid. An elastic anisotropy factor of 1.69 indicated moderate direction dependence, consistent with what has been reported for the cerium- and lanthanum-filled analogues of the same skutterudite family.

The electronic structure is where the material’s personality emerges. Multiple bands cross the Fermi level along the high-symmetry path, confirming metallic behavior, and the density of states shows a sharp peak at the Fermi energy dominated by praseodymium 4f states, with platinum 5d and germanium 4p orbitals hybridizing across a broader energy window. Spin-orbit coupling, essential for heavy elements like platinum, splits the platinum-derived bands and flattens them near the Fermi level, a signature of the heavy effective-mass carriers familiar from heavy-fermion physics. Charge-density maps on the (100) plane show praseodymium sitting in the cage voids with strong covalent Pt-Ge bonding forming the surrounding framework. Bader charge analysis quantified the bonding: praseodymium donates roughly 1.4 electrons and carries a strong cationic character, germanium accepts electrons as the main anion, and platinum remains only slightly positive. As temperature rises from 600 to 1400 kelvin, all charges drift mildly toward neutrality, a sign that thermal agitation slightly erodes the ordered charge transfer.

Magnetically, the compound is a quiet one. Spin-polarized calculations with the Hubbard correction gave a net moment of about 0.8 Bohr magnetons per formula unit, almost all of it contributed by the praseodymium atoms at roughly 0.74 Bohr magnetons, with platinum contributing about 0.01 and germanium essentially nothing. The small imbalance between spin-up and spin-down states near the Fermi level produces weak paramagnetism rather than ordered magnetism, which the authors note is compatible with the correlated metallic behavior seen in related heavy-fermion skutterudites. For spintronics, where controlling spin currents matters more than strong magnets, a material that combines metallic conduction, spin-orbit coupling and a tunable 4f moment is an interesting starting point, even if the magnetic signal here is subdued.

On the thermoelectric front, the results are honest about their limits. Using Boltzmann transport theory under the constant relaxation-time approximation with a relaxation time of 10⁻¹⁴ seconds, the team computed the Seebeck coefficient, electrical conductivity and electronic thermal conductivity across temperatures up to 1000 kelvin. The Seebeck coefficient oscillates in sign with doping and shrinks at high temperature as thermal broadening reduces carrier asymmetry. The lattice thermal conductivity, estimated with Slack’s semi-empirical model using a Grüneisen parameter of 2.05 and a Debye temperature near 280 kelvin, falls from about 3.8 to 1.2 watts per meter-kelvin between 300 and 1000 kelvin, reflecting the phonon scattering that the rattling praseodymium guest atoms promote. The dimensionless figure of merit ZT peaks at about 0.26 at 1000 kelvin near chemical potentials of plus or minus 0.35 electron volts. That is a moderate value, well below optimized commercial skutterudites, and the authors caution that the constant-relaxation-time approximation makes it an upper-bound estimate rather than a precise prediction. Co-doping or phonon engineering, they conclude, would be needed to make the material competitive.

The optical calculations reveal a more dramatic side. Across the 0 to 14 electron volt range, the dielectric function shows classic metallic behavior, with the real part negative at low energies and crossing zero near 1 electron volt, marking the plasma frequency. The imaginary part peaks near 8 electron volts, corresponding to interband transitions from occupied platinum and germanium p states into unoccupied hybridized states. The refractive index reaches about 9.5 at low energies, the absorption coefficient shows strong ultraviolet response with peaks at 8 and near 14 electron volts, and the optical conductivity displays a prominent Drude-like low-energy peak plus a sharp feature at 7.8 electron volts. Reflectivity in the infrared reaches about 0.6, suggesting the material could double as an infrared shield while absorbing ultraviolet light, a combination useful for devices that must manage thermal radiation carefully.

Perhaps the most forward-looking part of the study is the lithium storage analysis. Using a 2 by 2 by 2 supercell, the researchers identified candidate adsorption sites at high-symmetry interstitial voids and cage-centered positions, corresponding to Wyckoff positions 2a, 2c, 2d, 3b, 3e, 6e and 16e. Charge-density difference maps show electron accumulation around adsorbed lithium, and Bader analysis quantifies a transfer of 1.0 to 1.35 electrons per lithium atom depending on the site. The climbing-image nudged elastic band method found a migration barrier of roughly 250 millielectron volts between stable sites, comparable to established lithium-ion conductors that typically fall below 300 to 500 millielectron volts, implying good ionic mobility. The computed open-circuit voltage declines from 1.8 volts to about 0.1 volts at full lithiation, which the authors flag as approaching the lithium-plating risk zone familiar from graphite anodes. The theoretical capacity exceeds 200 milliampere-hours per gram, below graphite’s 372, and volume expansion at peak lithiation reaches about 8.5 percent, dramatically better than silicon’s roughly 300 percent swelling.

The authors are candid about the caveats. The platinum content makes commercial production economically impractical, and they call for platinum-free skutterudites that preserve the cage architecture with cheaper transition metals. The suspiciously smooth, linear voltage and capacity profiles suggest computational idealization that real structural disorder would complicate. And while the metallic band structure and weak magnetism echo traits of superconducting skutterudites, the study did not assess electron-phonon coupling, so any superconducting claim remains speculative. Thermodynamic calculations do support the material’s resilience, however: a cohesive energy of about minus 3.8 electron volts per atom, comparable to CoSb₃ and LaFe₄Sb₁₂, and free energy, entropy, heat capacity and enthalpy trends from 600 to 1200 kelvin consistent with a stable solid. Phonon dispersion calculations at 0 and 10 gigapascals show no imaginary frequencies, confirming dynamical stability.

What makes the study notable is not any single record-breaking number but the unified picture. The same cage that lets praseodymium rattle and scatter heat-carrying phonons also provides the interstitial voids that accept lithium ions, and the same 4f electrons that produce the magnetic moment dominate the states at the Fermi level that govern transport. In an era when energy conversion, storage and information processing are usually pursued with separate materials, a compound that credibly touches all of them, even at moderate performance levels, is worth the attention of experimentalists. The next step is clear: synthesize phase-pure PrPt₄Ge₁₂, ideally with modern techniques like spark plasma sintering that improve densification and microstructural control, and test whether the simulations survive contact with a real crystal.

Subject of Research: First-principles study of the structural, electronic, thermoelectric, magnetic, optical and lithium-ion storage properties of the filled skutterudite PrPt₄Ge₁₂

Article Title: Advanced computational insights of novel stable PrPt₄Ge₁₂ skutterudite for multifunctional optoelectronic, thermoelectric, spintronic and lithium-ion battery storage applications

Article References: Khan, M. A., Siyar, M., Jali, M. H., Saddiq, G., & Ullah, Z. (2026). Advanced computational insights of novel stable PrPt₄Ge₁₂ skutterudite for multifunctional optoelectronic, thermoelectric, spintronic and lithium-ion battery storage applications. Discover Chemistry, 3(1), Article 494. https://doi.org/10.1007/s44371-026-00934-9

Image Credits: AI Generated

DOI: 10.1007/s44371-026-00934-9

Keywords: skutterudite, PrPt4Ge12, density functional theory, thermoelectrics, lithium-ion batteries, spintronics, optoelectronics, heavy fermions, spin-orbit coupling, Boltzmann transport, energy storage, materials science

A team led by Qihang Liu and Xiaobing Chen of the State Key Laboratory of Quantum Functional Materials and the Department of Physics at Southern University of Science and Technology, together with the Quantum Science Center of the Guangdong–Hong Kong–Macao Greater Bay Area, has now turned that exercise into an automated workflow. Their open-source online platform, called FINDSPINGROUP, is reported in National Science Review. The tool places magnetic-moment arrangements and spin-orbit effects within a single, material-specific symmetry framework, allowing researchers to ask, in a consistent way, which responses a material’s magnetic geometry permits, and which additional responses emerge once spin-orbit coupling is switched on. The distinction is not academic. Knowing which mechanism drives a given response determines how that response will behave when the magnetic order is rotated, switched, or embedded in a different crystal environment, and it guides which materials deserve the expense of demanding calculations and experiments.

The conceptual heart of the platform is a reconciliation of two symmetry descriptions that have historically lived in separate regimes. In the absence of spin-orbit coupling, a magnetic material is described by a spin space group, in which operations acting on spins are not required to follow the corresponding rotations of the crystal lattice. Once spin-orbit coupling locks spin to lattice, the appropriate description becomes the magnetic space group, in which spin and lattice operations move together. Each map works well within its own regime, but the two are not automatically aligned. A spin space group is unchanged when the entire spin frame is rotated, so on its own it does not specify the physical orientation of spin operations relative to the crystal. A magnetic space group, by contrast, already assumes that this relationship is fixed. Different choices of unit cell, basis vectors, and origin add further complications, so comparing the two descriptions for a real material has meant identifying and realigning them by hand.

Liu and colleagues resolved this with the oriented spin space group, or OSSG. The OSSG selects the material-specific orientation of the spin operations relative to crystallographic directions, without itself introducing spin-orbit coupling. From this common starting point, two analyses branch out. The full OSSG provides symmetry constraints for the material without spin-orbit coupling, while the subset of operations that remain compatible with spin-lattice locking forms the corresponding magnetic space group and supplies the constraints that apply when spin-orbit coupling is included. Both branches generate crystallographic information and restrictions on magnetic and transport properties, and because both are expressed in the same coordinate frame, their predictions can be compared directly. “The important question is not only what symmetry a magnetic material has, but where each of its allowed responses comes from,” said Liu. “By placing magnetic geometry and spin-orbit effects in the same material-specific frame, the OSSG allows the two contributions to be compared directly.”

FINDSPINGROUP turns this framework into a practical pipeline. A user supplies a magnetic structure in CIF, MCIF, or the newly introduced SCIF format. The platform identifies the material-specific OSSG, converts the result to a standard crystallographic setting, matches it to a canonical database representative, and derives the corresponding magnetic space group in the same coordinate frame. It then interrogates the material with what amounts to two parallel questions: what does the magnetic geometry permit without spin-orbit coupling, and what additional responses become possible, or disappear, once spin-orbit coupling is included. To answer them, the software produces standard magnetic cells, spin Wyckoff positions, spin site-symmetry groups, spin Brillouin zones, and symmetry information at high-symmetry wave vectors. It evaluates whether magnetization, electric polarization, momentum-dependent spin polarization, spin texture, anomalous Hall conductivity, and nonlinear-response tensors are allowed in each regime.

Crucially, the platform returns symmetry constraints rather than numerical predictions. It does not calculate how large a Hall current or an electric polarization will be. Instead, it determines whether a response is symmetry-possible, which directions or tensor components are allowed, and whether its origin can be traced to magnetic geometry or to spin-orbit coupling. That separation of powers is what makes the tool useful as a screening instrument: it can eliminate candidates whose symmetry forbids a desired response before anyone invests in first-principles calculations or crystal growth, and it can flag candidates whose symmetry guarantees one. Combined with an online service, open-source code, and a searchable database, the workflow scales from the analysis of a single material to high-throughput searches across entire structural families.

The team demonstrated the approach on three materials, each posing a different puzzle. The first concerns spin splitting: does it always require spin-orbit coupling? The two-dimensional altermagnet V2Se2O shows that it does not. In this material, the magnetic geometry alone already permits momentum-dependent spin splitting of the electronic bands, a property once considered inseparable from spin-orbit physics. FINDSPINGROUP then tracks what changes when spin-orbit coupling is added: the symmetry is lowered, the allowed components of spin polarization change, and an additional magnetic response becomes permitted. The result is a complete symmetry account of how a purely geometric effect and a relativistic effect layer on top of one another in the same compound.

The second puzzle asks whether magnetic order can create electric polarization. In MnSe2, the arrangement of magnetic moments breaks the inversion symmetry of the underlying non-magnetic crystal, allowing an electric polarization to emerge. The same magnetic order also permits momentum-dependent spin splitting. Because multiple symmetry-related magnetic states satisfy the same constraints, FINDSPINGROUP identifies candidate switching endpoints, revealing whether the electric polarization and the spin-dependent responses can be reversed separately or must reverse together. That question bears directly on device design, since independent control of distinct order parameters is far more valuable than a single locked switch. The third puzzle concerns the anomalous Hall effect in the non-coplanar antiferromagnet CoNb3S6. There, the magnetic geometry permits a Hall response even without spin-orbit coupling, while forbidding spin polarization throughout the Brillouin zone. When spin-orbit coupling is included, additional spin polarization and magnetization become symmetry-allowed. Together, the three cases demonstrate why observing a ferromagnetic-like response does not, by itself, reveal its origin: superficially similar effects can obey different symmetry rules and respond differently to external control.

Reproducibility posed its own challenge, and the team addressed it with a new data standard. The spin crystallographic information file, or SCIF, extends the familiar CIF and MCIF formats by storing the crystal structure together with its spin-group assignment, symmetry operations, coordinate transformations, and metadata. Like its predecessors, SCIF is designed to make symmetry information portable between researchers, software packages, and databases. The team is working with the IUCr Commission on Magnetic Structures to develop SCIF as a community standard for exchanging spin-group information, a step that could spare future researchers the ambiguity of unit-cell choices and spin-frame conventions that has long complicated comparisons between published analyses.

FINDSPINGROUP is available as a web service at findspingroup.com, with source code hosted on GitHub, lowering the barrier for groups that lack specialized symmetry expertise. For the broader field of unconventional magnetism, the platform arrives at a moment of rapid expansion, as altermagnets, non-coplanar antiferromagnets, and magnetism-driven ferroelectrics compete for attention as next-generation spintronic materials. By making the paired symmetry analysis fast, standardized, and shareable, the tool shifts the field’s focus from cataloging exotic responses to classifying their mechanisms, a shift that could accelerate the search for materials whose magnetic geometry and spin-orbit physics can be controlled independently, and ultimately for devices that exploit each contribution on its own terms.

Subject of Research: Symmetry-based separation of magnetic-geometry and spin-orbit-coupling contributions to unconventional magnetic properties using oriented spin space groups

Article Title: How can scientists disentangle the origins of unconventional magnetic properties?

Article References: How can scientists disentangle the origins of unconventional magnetic properties?. (n.d.). Original publication

Image Credits: AI Generated

DOI: Not provided

Keywords: antiferromagnets, spin space group, oriented spin space group, magnetic space group, spin-orbit coupling, altermagnets, anomalous Hall effect, spin splitting, electric polarization, SCIF format, symmetry analysis, FINDSPINGROUP

The puzzle begins with a simple expectation. When a material enters the superconducting state, electrical resistance should drop to exactly zero as the temperature falls. Yet in a growing family of two-dimensional superconductors — including gate-tuned graphene systems — researchers have repeatedly observed regions where the resistance falls sharply but then saturates at a finite value instead of vanishing. These states show abrupt transitions out of the superconducting-like regime when temperature, magnetic field or current exceed critical thresholds, mimicking the phenomenology of true superconductivity. But the resistance never reaches zero. Theoretical physicists proposed in 1999 that such a ‘Bose metal’ could exist as a genuine quantum ground state, and a 2019 colloquium review catalogued the anomalous metal as a ‘failed superconductor’ seen in disordered films since the late 1980s. What has been missing is a clean, well-controlled system in which the state can be studied systematically.

The new experiment delivers exactly that. The team, led by Matthew Yankowitz at the University of Washington and Joshua Folk at the University of British Columbia, built devices from rhombohedral graphene — a stacked form of carbon in which the layers are aligned in the same lateral registry rather than the staggered arrangement of ordinary graphite. This stacking order produces flat electronic bands that amplify interactions between electrons, and rhombohedral graphene has in recent years become a prolific source of unconventional superconductivity. The researchers encapsulated their graphene in hexagonal boron nitride crystals supplied by Kenji Watanabe and Takashi Taniguchi of the National Institute for Materials Science in Japan, and placed it on a tungsten diselenide substrate that imparts strong spin–orbit coupling to the carbon electrons. Dual electrostatic gates allowed them to tune both the carrier density and the perpendicular electric field across the device with exquisite precision.

What they found was striking. At zero magnetic field, mapping the resistance across the full two-dimensional gate-voltage landscape revealed isolated pockets where the resistance dropped to zero — bona fide superconducting islands — embedded in a broader region of gate space where the resistance instead saturated at a finite value. Crucially, the two kinds of pockets displayed nearly identical phenomenology. Both showed sharp, abrupt transitions to the normal state as temperature was raised, as a perpendicular magnetic field was applied, or as the driving current was increased beyond a critical value. To any casual inspection, the two regimes looked like siblings. One simply carried current perfectly; the other did not.

The most dramatic twist came when the researchers applied a small magnetic field parallel to the plane of the graphene sheet. In conventional superconductors, an in-plane field has little effect because the field lines slip between the atomically thin layers without generating vortices. Here, however, a modest parallel field of a few hundred millitesla expanded the finite-resistance pockets and merged them with their zero-resistance neighbours, without qualitatively changing their behaviour. The result was a razor-sharp boundary, at millikelvin base temperature, between states of zero and finite resistance carved directly into the gate-voltage map. The superconducting pockets shrank while the anomalous-metal territory grew, suggesting that the parallel field gently tips the balance between the two competing phases rather than destroying either one outright.

The finite-resistance state reproduced the key experimental signatures that define the anomalous metal in thin-film superconductors. Most tellingly, the team measured a non-monotonic dependence on current: the differential resistance of the state varied in a complex, non-monotonic way as the applied direct current was swept, a hallmark previously documented in disordered films and Josephson-junction arrays. The researchers also performed a Berezinskii–Kosterlitz–Thouless analysis, examining how the voltage scales with current near the transition. In the true superconducting pocket, the current–voltage curves followed the expected cubic power law over a broad range, yielding a transition temperature of about 61 millikelvin. In the anomalous-metal pocket, the same criterion was never satisfied — the state flirts with superconducting order but never locks it in.

Why does this matter so much? The anomalous metal has been observed in quench-condensed aluminium films, granular metals, amorphous molybdenum–germanium films, electrostatically doped cuprate films, ion-gated two-dimensional superconductors, and hybrid semiconductor–superconductor Josephson arrays. In every previous case, the material contained substantial disorder, and skeptics could always argue that the finite resistance arose from sample-specific imperfections, inhomogeneous current paths, or heating effects rather than a genuine quantum state of matter. Ultra-clean rhombohedral graphene, with carrier mobility far exceeding that of any thin film and gate-tunable parameters that can be swept continuously, places severe constraints on all such extrinsic explanations. The state here is not an artifact of dirty metallurgy; it is an intrinsic property of a pristine quantum material.

The theoretical implications are equally profound. Proposed explanations for the anomalous metal invoke quantum fluctuations of the superconducting phase, dissipation from normal quasiparticles, a glassy tangle of superconducting vortices, or microscopic inhomogeneity that percolates superconducting islands into a resistive network. Each model makes different predictions about how the state should respond to magnetic field, current and disorder. The rhombohedral graphene platform, in which the superconducting and anomalous-metal pockets can be relocated, expanded and merged at will by turning gate voltages and applying small in-plane fields, offers a testing ground in which those predictions can be discriminated for the first time. The fact that the two phases share nearly identical critical behaviour — the same abrupt transitions, the same response to temperature and field — hints that they may be two faces of a single underlying quantum phase transition, separated by a boundary whose sharpness at base temperature suggests a genuine quantum critical line.

There is also a broader resonance with the wider graphene superconductivity programme. Since the 2018 discovery of unconventional superconductivity in magic-angle twisted bilayer graphene, the carbon family has yielded spin-polarized superconductors, chiral superconducting states, record violations of the Pauli paramagnetic limit, and superconductivity intertwined with ferroelectric orbital magnetism and topological charge order. The new result adds a crucial missing character to this cast: the anomalous metal, long confined to the margins of thin-film physics, now sits squarely within the same gate-tunable phase diagrams that host the most celebrated unconventional superconductors. Understanding why some pockets superconduct and others fail to do so — separated by nothing more than a small change in carrier density or electric displacement field — may reveal the microscopic ingredient that tips the balance, whether it be spin polarization, isospin texture, or the delicate interplay of flat-band kinetics and Coulomb repulsion.

For now, the anomalous metal remains without an accepted theoretical explanation, but the conditions of the hunt have fundamentally changed. A state once accessible only in disordered films of variable quality can now be dialled up on demand in an atomically clean, electrostatically programmable material, measured reproducibly across multiple devices and contact pairs, and probed with the full modern toolkit of quantum transport. As the authors and their collaborators — including theorists Boris Spivak, Steven Kivelson and Aharon Kapitulnik, whose work frames the field — continue to explore this system, the failed superconductor may soon give up its secrets. If it does, the answer will reshape our understanding not only of two-dimensional superconductivity but of the quantum phase transitions that govern how collective electronic order emerges, or collapses, at the coldest temperatures physics can reach.

Subject of Research: Anomalous metal and superconducting phases in rhombohedral graphene on a WSe2 substrate

Article Title: Anomalous metal and superconducting phases in rhombohedral graphene

Article References: Okounkova, A., Sohm, A., Faehndrich, T., Kumar, M., Waleffe, D., Yan, J., Watanabe, K., Taniguchi, T., Folk, J., & Yankowitz, M. (2026). Anomalous metal and superconducting phases in rhombohedral graphene. Nature. https://doi.org/10.1038/s41586-026-11033-1

Image Credits: AI Generated

DOI: 10.1038/s41586-026-11033-1

Keywords: rhombohedral graphene, anomalous metal, superconductivity, two-dimensional materials, quantum phase transition, gate tuning, spin–orbit coupling, Berezinskii–Kosterlitz–Thouless transition, failed superconductor, WSe2, quantum transport, flat bands

The study, led by Fatma Saad Saoud of Mohamed Elbachir El Ibrahimi University in Algeria, together with Rihab El Houda Djabou of the University of Galway in Ireland and Aldo H. Romero of West Virginia University in the United States, employed density functional theory to map how compression reshapes every aspect of cadmium iodide’s behavior. The team examined structural, electronic, vibrational, optical, and topological properties across a wide pressure range, using both the PBEsol and hybrid HSE06 exchange-correlation functionals to ensure their predictions were robust. Spin-orbit coupling was explicitly included throughout, a detail that matters enormously for heavy elements like iodine and cadmium, where relativistic effects can fundamentally alter the band structure.

At ambient pressure, the calculations place cadmium iodide’s indirect bandgap at 2.243 electronvolts without spin-orbit coupling and 2.047 electronvolts when relativistic effects are included. As pressure mounts, that gap shrinks continuously, driven by the increasing overlap between valence and conduction bands as the interlayer spacing collapses. By approximately 60 gigapascals, the gap closes entirely, marking a clean semiconductor-to-metal transition. The agreement between the two independent computational approaches lends considerable weight to this prediction, since hybrid functionals typically correct the bandgap underestimation that plagues simpler semi-local methods.

But a closing bandgap is only half the story. The researchers also probed the lattice dynamics of compressed cadmium iodide using density functional perturbation theory, asking whether the crystal would remain mechanically viable under such extreme conditions. Up to 40 gigapascals, the answer is a clear yes: no imaginary phonon modes appear anywhere in the Brillouin zone, and the phonon branches actually stiffen with pressure, a signature of strengthened bonding. Only at 60 gigapascals, precisely where the electronic gap vanishes, do imaginary phonon frequencies emerge around the L point of the Brillouin zone. This coincidence identifies 60 gigapascals as the critical threshold where the crystal structure itself begins to destabilize, meaning the most interesting electronic regime lies just below it.

That regime is where the study delivers its most striking result. At 40 gigapascals, with a finite global bandgap still intact, the team evaluated the Z2 topological invariant using the Fu-Kane parity criterion, which examines the symmetry eigenvalues of the occupied bands at the time-reversal invariant momenta of the Brillouin zone. The parity products yield a nontrivial invariant, confirming that compression has driven a band inversion and transformed cadmium iodide into a topological insulator. In such a material, the bulk is insulating, but the surface must host protected conducting states that cannot be removed without breaking time-reversal symmetry, a property that has fueled two decades of research into spintronics and fault-tolerant quantum computing.

The mechanism behind this transition is well understood in the topological materials community. Pressure compresses the crystal, enhancing the overlap between orbitals of different parity character. When the resulting band inversion flips the ordering of states near the Fermi level, the topology of the band structure changes, and the Z2 invariant switches from trivial to nontrivial. Similar pressure-driven topological transitions have been observed experimentally in materials such as lead-tin selenide alloys and bismuth halides, and the new work extends this design principle to a layered transition-metal dihalide, a chemically distinct and comparatively simple family of compounds.

The optical consequences are equally notable. The calculated absorption spectra show a pronounced enhancement in the ultraviolet region as pressure increases, with the absorption coefficient peaking at approximately 3.25 times ten to the fifth per centimeter at 40 gigapascals. Absorption coefficients of this magnitude indicate that compressed cadmium iodide could be an efficient ultraviolet absorber, a property relevant to photodetectors, ultraviolet sensing platforms, and energy conversion devices. The fact that this enhancement coincides with the topological window adds an intriguing multiplexing of functionalities: within a narrow pressure range, the material is simultaneously a strong ultraviolet absorber and a topological insulator.

For experimentalists, the predicted pressures are demanding but not unprecedented. Diamond anvil cells routinely reach tens of gigapascals, and 40 to 60 gigapascals falls within the accessible range for modern high-pressure laboratories. The authors are candid that the topological phase emerges only under relatively high pressures, but they frame their work as a theoretical foundation for future experiments and, importantly, as a roadmap for achieving the same physics under gentler conditions. Strain engineering in thin films, chemical substitution that mimics pressure through chemical pressure, and heterostructure design that imposes compression through lattice mismatch are all proposed as routes to realize the topological phase at ambient or near-ambient conditions.

The broader significance lies in the strategy itself. Rather than searching for new compounds, the study demonstrates that a well-known, structurally simple material can be reprogrammed through an external thermodynamic variable. Hydrostatic pressure acts as a continuous, reversible tuning knob that sweeps the material through ordinary semiconductor, topological insulator, and metal phases without altering its chemical composition. For sustainable technology applications, this suggests a path toward devices whose properties could be adjusted or switched by mechanical means, complementing the electric-field and optical gating that dominate current device architectures.

Cadmium iodide’s long history makes the result all the more compelling. The compound’s layered structure, with cadmium ions sandwiched between iodine planes held together by weak van der Waals forces, has made it a staple of textbook crystallography and a component in photographic and scintillator materials. That the same crystal harbors a hidden topological phase, waiting to be unlocked by compression, is a reminder that the materials catalog assembled over the past century remains far from fully explored. As the authors and the wider community pursue experimental confirmation and low-pressure analogues, cadmium iodide may yet find itself at the center of the next generation of optoelectronic and quantum device research.

Subject of Research: Pressure-induced electronic, optical, and topological phase transitions in layered cadmium iodide (CdI2) predicted by first-principles calculations

Article Title: Pressure-driven electronic, optical absorption, and topological phase transitions in CdI2 for sustainable optoelectronic and energy applications

Article References: Saad Saoud, F., Djabou, R. E. H., & Romero, A. H. (2026). Pressure-driven electronic, optical absorption, and topological phase transitions in CdI2 for sustainable optoelectronic and energy applications. Journal of Materials Science. https://doi.org/10.1007/s10853-026-13612-z

Image Credits: AI Generated

DOI: 10.1007/s10853-026-13612-z

Keywords: cadmium iodide, topological insulator, high pressure, density functional theory, band inversion, Z2 invariant, semiconductor-to-metal transition, phonons, ultraviolet absorption, optoelectronics, spin-orbit coupling, energy applications

The experiment, led by Shunfa Liu and Jin Liu at Sun Yat-sen University together with colleagues at the Institute of Semiconductors of the Chinese Academy of Sciences, Tianjin University, and Zhejiang University, centers on a deceptively simple architectural idea. Instead of placing a quantum dot at the center of a micropillar cavity — the standard position that couples to the fundamental, Gaussian-like mode — the team deterministically positioned a single epitaxial InAs quantum dot near the periphery of the pillar. There, the high-order transverse cavity modes possess precisely the kind of structured field profiles that the researchers wanted to exploit: vortex-like intensity distributions with phase singularities at the center and helical phase fronts that wind around the pillar axis. By positioning the dot where the structured mode field is strong, the team ensured that the quantum dot’s emission couples directly into these exotic modes rather than into the conventional fundamental one.

The technical heart of the work lies in the construction of four distinct structured cavity modes that are spectrally close to one another within a single wavelength-scale device. These modes, labeled M1 through M4, each carry a different spatial symmetry and polarization structure. When the quantum dot’s emission wavelength is tuned into resonance with one of these modes, the Purcell effect — the enhancement of spontaneous emission that occurs when an emitter sits inside a resonant cavity — acts selectively on the structured mode. The researchers demonstrated this tuning using a magnetic field applied in the Faraday configuration, which splits the neutral exciton transition of the quantum dot into two circularly polarized Zeeman branches. By sweeping the magnetic field, they could scan the quantum dot emission across the resonances of the structured modes M2 through M4, achieving mode-selective coupling with remarkable control.

The quantitative results underline how efficiently this structured coupling works. For one representative device, the team measured a far-detuned exciton lifetime of 959.1 picoseconds. When the quantum dot was tuned into resonance with the M3 mode, the lifetime collapsed to 70.9 picoseconds, corresponding to a measured Purcell enhancement factor of approximately 12.5. Tuning to the M2 resonance yielded a lifetime of 124.1 picoseconds and a Purcell factor of about 6.7. Critically, the emission remained a stream of single photons: second-order correlation measurements gave g^(2)(0) values of 0.059 and 0.021 in the two circular polarization channels at resonance, comfortably below the 0.5 threshold that certifies single-photon purity and indicating near-ideal single-photon emission in both channels simultaneously.

The most striking outcome is the spin-locked chiral orbital angular momentum of the emitted photons. Orbital angular momentum, or OAM, endows light with a helical phase structure described by an integer topological charge; such twisted photons are the basis of high-dimensional quantum information protocols. Previous demonstrations of OAM single-photon sources relied on spiral gratings, metasurfaces, or metalenses appended to quantum emitters, approaches that typically suffer from low quality factors, large footprints, or unwanted superpositions of OAM states. In the new work, the chirality emerges intrinsically from the cavity itself. When the Zeeman-split quantum dot transition couples to the M3 vortex mode, left-circularly-polarized emission carries an OAM of l = −1 while right-circularly-polarized emission carries l = +1. The spin of the emitted photon — its circular polarization — is thus locked to its orbital angular momentum, a hallmark of chiral quantum optics realized in a device no larger than a few micrometers across.

Verifying this behavior demanded sophisticated single-photon-level characterization. The researchers projected the emitted photons onto a vortex waveplate basis with topological charges ranging from −4 to +4, capturing the resulting images with an electron-multiplying CCD camera. The demodulated images confirmed unambiguously that the emitted single photons carried the expected OAM orders in each circular polarization channel. Simulations reinforced the picture: projecting the far-field emission onto the helical phase basis showed that the photons retain approximately 99 percent OAM purity over a broad range of quantum dot positions around the optimal coupling points. Even more practically, the calculations revealed that realistic positioning errors of several tens of nanometers leave both the Purcell factor and the collection efficiency essentially unchanged — a crucial tolerance for any scalable fabrication scheme.

Beyond spin-locked OAM, the platform also delivers tunable spin–orbit entanglement within a single photon. When the quantum dot was tuned into resonance with the M2 and M4 modes instead, the emission populated superpositions of the structured mode pairs, producing internal entanglement between the photon’s polarization and its orbital angular momentum degrees of freedom. The team characterized these states using full quantum state tomography, employing a vortex waveplate and a sequence of quarter-wave plate, half-wave plate, and polarizer projections across sixteen measurement bases spanning both polarization and OAM Hilbert spaces. Because the entanglement structure depends on which structured mode the dot is coupled to, and because that coupling is magnetically tunable, the degree and character of the spin–orbit entanglement can be engineered at will — a level of control that no previous single-photon source based on quantum dots has offered in a single monolithic device.

The collection efficiency numbers make the platform genuinely attractive for applications. Simulations show that near the optimal coupling positions, roughly 77 percent of the emitted light in the selected spin–orbit channel can be gathered within the numerical aperture of a standard high-NA objective, and at the experimental NA of 0.65 the M3 collection efficiency approaches saturation, comparable to that of the fundamental mode. Higher-order simulations point the way forward: coupling to modes such as M6 and M8 would generate topological charges of l = +2 and l = −3 respectively, with calculated circular-polarization fractions of 99.61 and 93.79 percent, suggesting that the same architecture can be extended to a whole ladder of higher-dimensional photonic states without any additional phase-shaping optics.

The implications ripple across several fields. In chiral quantum optics, where directionality and spin-dependent light–matter coupling underpin nonreciprocal single-photon devices and spin-photon interfaces, this work provides a solid-state, electrically compatible platform with intrinsic spin–orbit locking. In high-dimensional quantum communication, where encoding information in OAM states multiplies channel capacity and improves noise resilience, the availability of bright, cavity-enhanced, single-mode twisted single photons with purity values approaching g^(2)(0) ≈ 0.02 addresses long-standing bottlenecks in source quality and footprint. And because the entire interaction unfolds inside a wavelength-scale semiconductor micropillar — a device class already compatible with wafer-scale fabrication and deterministic positioning techniques — the path toward arrays of entangled twisted-photon emitters looks genuinely plausible. The authors note that their data and codes are openly available, and the broader research program, which includes recent demonstrations of nanophotonic quantum skyrmions in related micropillar systems, suggests that structured quantum light is rapidly moving from a theoretical curiosity to an engineering discipline. What was once the scalar workhorse of cavity QED has become a fully vectorial, structured, and chiral quantum stage — one where every photon emitted carries not just energy and polarization, but a carefully scripted twist.

Subject of Research: Structured light–matter interaction at the single-photon level in a semiconductor quantum-dot micropillar cavity quantum electrodynamics system

Article Title: Structured light–matter interaction in semiconductor cavity quantum electrodynamics

Article References: Liu, S., Ma, J., Liu, H., Wang, Y., Li, X., Ni, H., Niu, Z., Zou, K., Meng, Y., Hu, X., Wang, X., & Liu, J. (2026). Structured light–matter interaction in semiconductor cavity quantum electrodynamics. Nature Nanotechnology. https://doi.org/10.1038/s41565-026-02275-1

Image Credits: AI Generated

DOI: 10.1038/s41565-026-02275-1

Keywords: cavity quantum electrodynamics, quantum dots, orbital angular momentum, single photons, spin–orbit coupling, chiral quantum optics, micropillar cavities, Purcell effect, quantum entanglement, structured light, semiconductor photonics, quantum information

Bismuth atoms, positioned near lead on the periodic table, possess significantly heavier nuclei. This increased mass forces their orbiting electrons to move at relativistic speeds — velocities approaching that of light — thereby bringing Einstein’s theory of relativity into play. At these speeds, electrons no longer behave as independent particles with separate spin and orbital motion. Instead, their spin becomes intertwined with their orbit in a phenomenon called spin-orbit coupling, fundamentally altering electron interactions and the nature of chemical bonds.

This nuanced coupling blurs the distinction between sigma and pi bonds, transforming how bonds form and behave. Researchers led by Professor Lai-Sheng Wang conducted experiments on carbon-bismuth molecular ions cooled near absolute zero, analyzing them via advanced photoelectron spectroscopy. This technique knocks electrons from the molecule with laser light and measures their energy to uncover the nature of bonding.

Contrary to traditional models, the spectroscopy data revealed that the bonds in these heavy-element molecules do not conform to one sigma and two pi bonds. Instead, the bonding structure appears as one pi bond combined with two hybrid sigma-pi bonds, a direct signature of relativistic effects modifying chemical bonding. “The boundary between sigma and pi bonds is now smeared,” explains Wang, highlighting a radical departure from classical bonding paradigms.

The implications of this discovery extend beyond academic interest. As other heavy elements gain prominence in materials science—including in quantum computing and solar cell technologies—understanding these relativistic bonding effects could lead to breakthroughs in designing novel materials. Bismuth, already poised as a less toxic alternative to lead, emerges as a compelling candidate in the next generation of quantum materials and sustainable technologies.

Wang and his team believe this spectroscopic evidence represents a pivotal moment for chemists worldwide. The findings challenge longstanding assumptions and may necessitate updates to chemistry curricula and textbooks, acknowledging that the classical dichotomy of sigma and pi bonds does not hold universally, especially under relativistic regimes.

Funded by the U.S. National Science Foundation and Department of Energy, this research bridges atomic physics, quantum mechanics, and chemistry, illustrating a profound example where relativity shapes the microscopic world of chemical bonds.

Subject of Research: Chemical bonding in heavy elements influenced by relativistic effects
Article Title: Relativistic collapse of the classical triple bond in the CBi− molecular ion
News Publication Date: 9-Jul-2026
Web References: http://dx.doi.org/10.1126/science.aei1285

Keywords
Relativistic effects, chemical bonding, bismuth, heavy elements, spin-orbit coupling, photoelectron spectroscopy, quantum materials