The Berry curvature describes how the quantum phase of an electron’s wavefunction twists as the electron moves through momentum space. Inside a crystal, an electron accelerated by an electric field normally acquires only a longitudinal velocity along the field, with a magnitude set by the energy band dispersion. In the presence of a magnetic field, the Lorentz force adds a transverse Hall velocity. Remarkably, electrons can also acquire such a transverse, anomalous velocity with no magnetic field at all, simply by travelling through regions of reciprocal space where the Berry curvature is non-zero. The electron wave-packet velocity contains a term given by the cross product of the crystal momentum’s time derivative and the Berry curvature vector, producing a circular component of motion. Because the electric field of light drives both the longitudinal and transverse components of the electron’s velocity, a natural question arises: is there a direct link between the Berry curvature and the conservation of angular momentum in light-matter interactions?

The symmetries of a crystal make this question even more compelling. Space inversion symmetry requires the Berry curvature to be identical at opposite points in momentum space, while time-reversal symmetry requires it to be exactly opposite. Breaking time-reversal symmetry therefore lifts the degeneracy between valleys, the distinct energy minima that give two-dimensional semiconductors their valleytronic properties. The Berry curvature, together with the quantum metric and their momentum-space derivatives, forms the quantum geometric tensor of the electronic states, and these quantities govern circular dichroism, valley-contrasted optical selection rules, the valley Hall effect, the nonlinear Hall effect and the bulk photovoltaic effect. Although the momentum-resolved Berry curvature is straightforward to compute from the matrix elements of Bloch wavefunctions, a direct experimental measurement of this fundamental quantity has remained extremely challenging.

Previous studies have offered partial glimpses. Seminal work on photoluminescence gave a microscopic interpretation of valley circular dichroism based on the valley-contrasting Berry curvature, and recent high-harmonic generation experiments explored the interplay between Berry curvature and strong-field nonlinear optics, often using transition metal dichalcogenides as model systems. None of these works, however, provided an analytical expression that quantitatively relates an experimentally accessible all-optical response to the Berry curvature. The only direct measurement proposed so far relied on spin-resolved circular dichroism in angle-resolved photoemission spectroscopy, an approach whose range of validity is still under discussion. What has been missing is a quantitative, broadly accessible tabletop probe with ultrafast time resolution.

The new work fills this gap with a remarkably clean theoretical result. Working in a two-band picture with a single vertical optical transition at a well-defined crystal momentum, the researchers show that the circular dichroism of the mth harmonic, defined as the normalized difference between the intensities of the harmonic polarization generated for the two opposite light helicities, equals the local Berry curvature at the resonant momentum divided by the squared interband dipole matrix element. This equation is general and imposes no symmetry-related restrictions, provided the relevant energy levels are sufficiently well separated to prevent overlapping resonances from multiple momentum points. The requirements are simply that the relevant harmonics exist, even harmonics being forbidden in the electric dipole approximation when inversion symmetry is preserved, and that a single optically accessible resonance can be treated as an effective two-level system. The formalism applies not only to direct-gap semiconductors but to any system where a resonant vertical transition drives a harmonic response, and it extends the known connection between linear circular dichroism and Berry curvature into the nonlinear regime.

To connect this idealized result to a realistic experiment, the team turned to monolayer tungsten diselenide, a prototypical transition metal dichalcogenide with two energetically degenerate valleys at opposite momenta. An off-resonant circularly polarized pump beam breaks time-reversal symmetry through the coherent, valley-exclusive optical Stark and Bloch-Siegert effects, lifting the valley degeneracy by roughly ten millielectronvolts under typical conditions. A linearly polarized probe beam resonant with half the optical band gap then generates a second-harmonic signal. The researchers derived an analytical expression showing that the resulting second-harmonic circular dichroism is proportional to the sum of the pump-dressed Berry curvatures of the two valleys, weighted by valley-resolved resonance denominators. The signal scales quadratically with the pump field amplitude, flips sign when the pump helicity is reversed, and depends on the probe detuning through a complex resonance factor that encodes the dephasing time of the optical transition.

The theory also delivers a striking symmetry insight. Expressed in terms of the Cartesian components of the second-order nonlinear susceptibility, the second-harmonic circular dichroism requires that two susceptibility components are non-zero and, crucially, out of phase with one another, a condition that cannot be deduced from a purely macroscopic description of the nonlinear tensors. When time-reversal symmetry is preserved, the effect can only appear in point groups 1, 3 and bar-6, where circular second-harmonic generation is allowed by momentum conservation. With time-reversal symmetry broken, the effect becomes allowed for all non-centrosymmetric magnetic groups with one- or threefold rotational symmetry, including the symmetry of monolayer transition metal dichalcogenides. The asymmetry between energy levels and Berry curvature at opposite momenta induces the phase mismatch between the susceptibility components, linking macroscopic crystal symmetries directly to the microscopic quantum geometry of the electronic bands.

The experimental demonstration was performed in a two-colour pump-probe geometry on a mechanically exfoliated WSe2 monolayer, using synchronized optical parametric oscillators delivering roughly 100-femtosecond pulses at pump and probe wavelengths of 1,800 and 1,460 nanometres. Helicity-resolved spectra revealed the second harmonic of the pump beam appearing exclusively in the cross-polarized detection channel, as expected from spin angular momentum conservation, while the second harmonic of the probe beam showed a clear difference between left and right circular detection at zero pump-probe delay. The incoherent two-photon photoluminescence, which overlaps spectrally with the probe second harmonic, cancels exactly in the helicity difference, leaving a clean dichroism signal. The response is ultrafast, vanishing on a timescale set only by the pulse durations, with a fitted Gaussian full-width at half-maximum of 313 plus or minus 40 femtoseconds, and it disappears entirely when the pump beam is linearly polarized, confirming that broken time-reversal symmetry is the origin of the effect.

By scanning the pump intensity, the pump-probe delay and the probe wavelength, the team verified every prediction of their analytical model, including the quadratic intensity scaling and a sign reversal of the dichroism as the second-harmonic wavelength was tuned across the light-dressed valley resonances. Because every variable in the model except two was independently measured, fitting the wavelength dependence yielded direct estimates of the dephasing time, 42 plus or minus 11 femtoseconds, and the resonant Berry curvature at the valleys, 6.2 plus or minus 1.4 square angstroms, in good agreement with values from tight-binding and density functional theory calculations. The work establishes second-harmonic circular dichroism as a non-invasive, ultrafast and all-optical probe of the local Berry curvature, and it points toward ultrafast devices that combine spin and valley degrees of freedom with the engineering and readout of quantum geometry, advancing the emerging field of ultrafast all-optical valleytronics.

Subject of Research: Nonlinear circular dichroism as an ultrafast all-optical probe of the local Berry curvature in monolayer WSe2

Article Title: Nonlinear circular dichroism reveals the local Berry curvature

Article References: Nonlinear circular dichroism reveals the local Berry curvature. (n.d.). https://doi.org/10.1038/s41566-026-02025-8

Image Credits: AI Generated

DOI: 10.1038/s41566-026-02025-8

Keywords: Berry curvature, circular dichroism, high-harmonic generation, second-harmonic generation, WSe2, valleytronics, time-reversal symmetry, quantum geometry, nonlinear optics, ultrafast photonics, optical Stark effect, transition metal dichalcogenides

The central challenge the researchers set out to solve is a familiar one in nanophotonics. Two-dimensional semiconductors such as WSe2 host tightly bound electron-hole pairs called excitons, which possess large oscillator strengths and make these materials attractive for photodetectors, light emitters, valleytronics, and quantum technologies. Yet because the material is only one atom thick, its overlap with free-space light is vanishingly small. Conventional dielectric resonators, including photonic crystals, microring resonators, and distributed Bragg reflector cavities, confine light only to diffraction-limited volumes, which limits how strongly the cavity field can interact with the monolayer. Plasmonic structures can squeeze light into nanoscale gaps, but the ohmic losses in metals reabsorb photons and degrade the coherence that quantum applications demand.

The Purdue-Harvard collaboration turned to photonic inverse design, specifically adjoint-based topology optimization, to escape this trade-off. In this approach, a computer algorithm iteratively reshapes the distribution of silicon and air within a metasurface unit cell to maximize the electric-field intensity at a target point on the surface. Each optimization cycle consists of a forward electromagnetic simulation, an adjoint simulation driven by a virtual dipole at the target location, and a gradient-based update of a continuous material-density field. Gaussian filtering and a progressively sharpened Heaviside projection push the design toward binary, manufacturable patterns, with roughly 200 to 250 iterations required before the figure of merit saturates. Strikingly, regardless of the random starting point, the algorithm consistently converged on a bowtie-like gap at the center of each unit cell, suggesting that this geometry represents a global optimum for field concentration.

The resulting cavities were fabricated from 100 to 200 nanometer-thick silicon layers on sapphire substrates using electron beam lithography and reactive ion etching. Simulations of the ideal designs predicted local field-intensity enhancements exceeding 50-fold relative to the incident field, with an effective mode volume of approximately 30 by 30 by 100 cubic nanometers, corresponding to roughly one 2500th of a cubic wavelength. The optical hotspots sit directly beneath where the WSe2 monolayer would rest, ensuring deterministic coupling between the excitons and the confined cavity mode. Because the cavities are supported on a substrate rather than suspended as membranes, they are mechanically robust and well suited to the scalable integration of van der Waals materials.

Experimentally, the team transferred large hexagonal boron nitride-encapsulated WSe2 monolayers, roughly 40 by 30 micrometers in area, onto arrays of these cavities using a gold-assisted exfoliation and transfer technique. Each flake was positioned so that part of it lay on the cavity array and part on adjacent unpatterned silicon, enabling a direct on-chip comparison between cavity-coupled and reference emission. Raman spectroscopy confirmed that strain induced by the underlying pattern was negligible, with peak shifts below one wavenumber. Photoluminescence maps then revealed bright, reproducible emission from the cavity regions: raw enhancements of approximately 6-fold, 14-fold, and, for the best-performing array, nearly 28-fold were measured across three different cavity designs, with a consistent average of about tenfold. When normalized to the tiny effective hotspot area, this corresponds to a per-area enhancement on the order of one thousand.

Numerical simulations that incorporated realistic material absorption and the actual shapes extracted from scanning electron microscope images helped explain why the measured enhancement fell short of the ideal 50-fold prediction. The small feature sizes and dense patterning amplify proximity effects during electron beam lithography, and etching introduces roughness that scatters light and degrades field localization. Loading the cavity with the WSe2 and boron nitride stack further broadens and shifts the resonance. When all of these imperfections were included, the simulated near-field enhancement dropped to approximately tenfold, in close agreement with the experimental photoluminescence results and the observed lifetime shortening. The simulations also showed that emitters placed in the hotspot radiate highly directional light, with much of the power falling within the collection cone of a standard high-numerical-aperture microscope objective, whereas emitters on flat silicon radiate mostly at grazing angles.

Perhaps the most intriguing findings came from time-resolved photoluminescence measurements. Using femtosecond pulsed excitation, the researchers found that exciton decay on the cavities became strongly non-exponential at all pump powers, while decay on the flat reference regions remained nearly exponential except at the highest powers. Fitting the decay curves with a mixed model combining a stretched exponential and a single exponential revealed a stretching parameter of roughly 0.38 on the cavity, very close to the value of one third expected for two-dimensional dipole-dipole energy transfer between excitons. Off the cavity, the stretching parameter started near 0.8 at low power and decreased as excitation increased. The team also measured an approximately eightfold shortening of the exciton lifetime on the cavity, consistent with Purcell-enhanced radiative decay.

The power dependence of the decay dynamics pointed to cavity-mediated exciton-exciton interactions as a dominant mechanism. A biexcitonic recombination model best described the shortening of the effective decay time with pump power, and the extracted biexcitonic recombination coefficient on the cavity was more than an order of magnitude, about 33 times, larger than off the cavity. By concentrating optical near fields into nanoscale hotspots, the cavities increase the local exciton density and strengthen resonant dipole-dipole interactions, effectively amplifying many-body excitonic phenomena that are normally difficult to access. Saturation measurements reinforced this picture: emission on the cavity saturated at 20 microwatts of pump power, five times lower than the 100 microwatts required off the cavity, indicating substantially enhanced excitonic nonlinearities.

Low-temperature spectroscopy added further richness. Between 5 and 200 kelvin, the cavity-coupled monolayers displayed a well-resolved manifold of excitonic states, including bright excitons, trions, biexcitons, and defect-bound excitons, with noticeably narrower linewidths on the cavity than on the flat substrate. The presence of trions, which normally require deliberate gate-controlled doping, revealed unintentional electron doping introduced during the gold-assisted transfer, at densities estimated between ten to the eleventh and ten to the twelfth per square centimeter. Notably, defect-bound exciton emission, which persisted even to room temperature, exhibited unexpectedly short lifetimes on the cavity, roughly half those of the bright excitons, and about twice shorter on the cavity than off it at every detection wavelength.

The researchers emphasize that the reported raw enhancement values are the most physically meaningful metric for practical applications, even though normalized figures are conventionally used to compare across studies. Compared against previously reported plasmonic enhancements of WSe2 emission, the dielectric platform is competitive while preserving coherence and enabling efficient light extraction. The work establishes topology-optimized silicon-on-sapphire cavities as a versatile, CMOS-compatible alternative to plasmonics for controlling exciton-photon and exciton-exciton interactions, and the authors anticipate that the platform will accelerate the integration of van der Waals semiconductors into scalable quantum photonics, opening routes toward cavity-enabled quantum many-body physics, valley-selective emission, and unprecedented excitonic nonlinearities, with a detailed study of enhanced two-photon nonlinearities planned as a follow-up.

Subject of Research: Topology-optimized dielectric nanocavities enhancing excitonic light emission and exciton-exciton interactions in monolayer WSe2

Article Title: Topology-optimized dielectric cavities for enhanced excitonic light emission from WSe2

Article References: Matthiessen, O., Triplett, B., Yesilyurt, O., Cassara, D., Pagadala, K., Yang, M. M., Llacsahuanga Allcca, A. E., Ather, H., Fruhling, C., Solanki, A. B., Chen, Y. P., Alaeian, H., Kildishev, A. V., Shalaev, V. M., Capasso, F., Boltasseva, A., & Mkhitaryan, V. (2026). Topology-optimized dielectric cavities for enhanced excitonic light emission from WSe2. Light: Science & Applications, 15(1), Article 387. https://doi.org/10.1038/s41377-026-02436-w

Image Credits: AI Generated

DOI: 10.1038/s41377-026-02436-w

Keywords: WSe2, topology optimization, dielectric cavities, nanophotonics, excitons, photoluminescence, Purcell enhancement, two-dimensional semiconductors, inverse design, quantum photonics, silicon photonics, light-matter coupling

The heart of the device is a tri-layer stack of tungsten diselenide, a semiconductor only a few atoms thick that belongs to the family of transition metal dichalcogenides. Two-dimensional materials like WSe2 are prized in neuromorphic engineering because their entire volume sits at the surface, making their electronic properties exquisitely sensitive to light, electric fields and chemical modification. In their native form, however, WSe2 devices often fall short of the stable, tunable conductance states that artificial synapses demand. The researchers solved this by treating the material with benzyl viologen, a strong electron-donating molecule that donates charge to the WSe2 lattice and shifts its Fermi level, effectively engineering the carrier polarity of the channel and setting the stage for the dramatic optical behaviors that follow.

Before any synaptic claims could be made, the team had to prove the material survived the doping process intact. Atomic force microscopy confirmed the structural integrity and surface morphology of the tri-layer films, while Raman spectroscopy verified that the crystal lattice remained high quality after exposure to the benzyl viologen treatment. On the electrical side, gate-dependent transfer curves and current-voltage measurements mapped out how the doping transformed the device’s behavior, and the researchers constructed an energy band diagram showing the Fermi level shift that the molecular dopants induce. This combination of structural and electrical characterization matters because any degradation of the delicate 2D lattice would undermine the reproducibility that real neuromorphic circuits require.

The most striking results emerge when light hits the device. The BV-doped WSe2 synapse responds strongly to both visible and deep-ultraviolet illumination, but it is the deep-ultraviolet response that gives the device its memory. Under DUV light, charges become trapped within the material system, and these trapped charges persist long after the light is switched off, producing a stable conductance state that functions as a nonvolatile memory. In other words, a flash of ultraviolet light writes information into the device, and the device holds that information without power, much as a biological synapse retains the trace of a past experience. This optically programmable memory is what allows the same physical structure to act simultaneously as a photodetector and a synaptic element.

When stimulated with sequences of optical pulses rather than continuous illumination, the device reproduces hallmark behaviors of biological synapses. Paired-pulse facilitation, a form of short-term plasticity in which the second of two closely spaced signals produces a larger response than the first, appears naturally in the device’s conductance dynamics. With longer or more intense stimulation, the device exhibits long-term potentiation and long-term depression, the persistent strengthening and weakening of connection strength that neuroscientists consider the cellular basis of learning and memory. Crucially, the magnitude of the response is tunable: by controlling the duration of the deep-ultraviolet pulses, the researchers increased the device’s photoresponse from 25.2 percent to 1438.7 percent, a dynamic range wide enough to encode many distinct synaptic weights.

That tunability translates directly into computational capability. The team demonstrated that the device can perform a logic OR gate operation, outputting a high signal when either of two inputs is present, and that it can carry out selective alphabet recognition, distinguishing among written characters based on the optical signatures stored in its conductance states. These demonstrations show that the device is not merely a passive memory element but an active processing unit, capable of the kind of in-memory logic that could dramatically reduce the energy overhead of edge-computing systems, where data must be processed locally under strict power budgets rather than shipped to energy-hungry data centers.

To test whether the device’s synaptic behavior could scale to meaningful machine learning, the researchers implemented its experimentally measured synaptic weight characteristics in an artificial neural network and trained that network to identify handwritten digits from the MNIST dataset, a standard benchmark in computer vision. The simulated network achieved an accuracy of 92 percent, and the team validated the learning process through epoch-dependent learning curves and confusion matrix analysis, confirming that the network’s errors were distributed in the way one expects from a genuinely learning system rather than a lucky configuration. The result is significant because it grounds the device physics in a concrete application: the same conductance modulation that the researchers measured in the laboratory can, in principle, serve as the adjustable weights that artificial neural networks rely on.

The broader significance of the work lies in its multifunctionality. Most neuromorphic devices reported to date specialize in one role, whether as memristors, phase-change memories or electrochemical transistors, and require separate photonic or electronic circuitry to interface with the outside world. By combining optical sensing, nonvolatile charge-trapping memory, short- and long-term plasticity, logic operation and pattern recognition in a single doped 2D material platform, the WSe2 synapse points toward integrated intelligent sensors that could see, remember and compute in one package. Such devices would be natural fits for autonomous drones, biomedical implants and environmental monitors, where every milliwatt saved extends operational life.

There are, of course, hurdles between a laboratory demonstration and deployable technology. The device relies on exquisitely controlled chemical doping of atomically thin crystals, and scaling such processes to wafer-scale manufacturing while maintaining the uniformity that large neural networks demand remains an open challenge in the 2D materials community. The 92 percent MNIST accuracy, while respectable, still trails the best software-based networks, suggesting that device variability and nonlinearity in the conductance updates will need further engineering. The published version of the paper is also an early-release, peer-reviewed accepted manuscript that may undergo further edits before the final version of record appears, so specific figures could be refined.

Even so, the study adds an important entry to the growing catalog of optoelectronic synapses, and its use of benzyl viologen doping to engineer carrier polarity in tri-layer WSe2 gives other researchers a concrete chemical lever to pull. The work was supported by the Korea Basic Science Institute through a National Research Facilities and Equipment Center grant funded by the Korean Ministry of Education, by an IITP Information Technology Research Center grant from the Ministry of Science and ICT, and by the ongoing research funding program of King Saud University in Riyadh. As artificial intelligence migrates from the cloud toward the edge, devices that can be programmed by nothing more than pulses of light, and that learn the way neurons do, may prove to be exactly the kind of hardware the next generation of intelligent machines is waiting for.

Subject of Research: Optoelectronic synaptic devices based on doped two-dimensional tungsten diselenide for neuromorphic computing and logic operations

Article Title: A multifunctional optoelectronic synaptic device for logic operation and neuromorphic computing

Article References: Dastgeer, G., Nisar, S., Fatima, I., Ali, R. F., Rabani, I., Hussain, K., Alsalme, A., & Eom, J. (2026). A multifunctional optoelectronic synaptic device for logic operation and neuromorphic computing. Advanced Composites and Hybrid Materials. https://doi.org/10.1007/s42114-026-02103-z

Image Credits: AI Generated

DOI: 10.1007/s42114-026-02103-z

Keywords: neuromorphic computing, optoelectronic synapse, tungsten diselenide, WSe2, benzyl viologen doping, two-dimensional materials, memristor, synaptic plasticity, charge trapping, artificial neural network, MNIST, logic gates

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