Predicting the critical temperature ($T_c$) of superconducting materials is central to the search for new superconductors. Conventional machine learning models depend on handcrafted descriptors, while existing graph neural networks do not jointly exploit superconducting category information and physicochemical statistics. We introduce the Hierarchical Graph $T_c$ Network (HGTC-Net), a joint classification-regression framework for $T_c$ prediction. Crystal structures from the 3DSC database are converted into graph representations whose node and edge features encode local atomic environments and interatomic interactions. An HSC-XGB module performs hierarchical superconducting classification, including binary identification and family recognition. The resulting category probabilities are injected into the PriorGNN regression model through a gating mechanism that guides graph representation learning and $T_c$ prediction. The model attains coefficients of determination $R^2=0.9065$ and 0.8809 on the training and test sets, respectively. The framework is further applied to 84 461 candidate structures from the GNoME database for external screening of previously unseen compounds. HGTC-Net therefore provides a route for screening high-$T_c$ superconductors.

Elastic waves propagating can be regulated and synthesized to realize rich non-Abelian phenomena and topological phases of solid media. Therefore, this work investigates the noncommutative mechanical responses and non-Abelian nodal braiding in three-dimensional elastic wave metamaterials with duality symmetry. The connection between dispersion relation and twisting angles is derived by lattice dynamics and next-nearest-neighbor interaction. Then, the duality transformation and self-dual conditions are revealed by geometric correspondence and the root-finding algorithm. Based on the semiclassical equations of motion and polarized pseudospin states, the spin phase evolution is obtained. The noncommutative propagation paths of the wave packet in real and reciprocal space are achieved as well. In addition, the quaternion charges and patch Euler classes can be calculated by loops encircling the nodal points and patches penetrating the nodal lines, respectively. They can characterize the non-Abelian topological properties of the nodal lines and predict topological phase transitions, i.e., nodal stability. The nontrivial braiding of nodal links in momentum and parameter space is revealed numerically by structural parameters. Experiments further support the bulk-edge correspondence and the presence of the gap node.

In altermagnets and fully compensated ferrimagnets, not only the electron band but also the magnon band exhibits spin splitting without net magnetization, which enables thermal activation of the magnon spin current. Here, we theoretically investigate magnetic field effects on the magnon properties of these antiferromagnets in the presence of weak easy-axis anisotropy which makes the collinear states robust against the magnetic field. For the altermagnet and compensated ferrimagnet, we analyze a two-sublattice order in the $J_1\text{−}{J}_2\text{−}{J}_2^{\prime }$ model on the square lattice and a triple-$\mathbf{Q}$ 12-sublattice order in the $J_1\text{−}{J}_3$ model on the kagome lattice, respectively, each accompanied by $d$- and $s$-wave spin splitting at zero field. It is shown that, for positive (negative) magnetic field $H$ whose energy scale is smaller than the anisotropy gap, the up- and down-spin magnon bands are shifted to lower (higher) and higher (lower) energies, respectively, like the Zeeman coupling in electron systems. In the altermagnet, with increasing field, $d$-wave splitting tends to be deformed into $s$-wave splitting, which is reflected as the change in the direction of the spin current generated by thermal gradient. In the compensated ferrimagnet, the $s$-wave nature, i.e., the population imbalance between the up- and down-spin magnons at $H=0$, can induce asymmetric field dependence of the longitudinal spin and thermal conductivities in a field-sweep process.

Floquet engineering, which involves controlling systems through time-periodic driving, is a method for coherently manipulating quantum materials and realizing dynamical states with novel functionalities. Most research in solid-state systems has focused on the use of ac-electric fields as the controlling drive. In this study, we investigate the effects of ac-magnetic fields on two-dimensional (2D) Dirac electrons and report the emergence of new states and new transport phenomena. In a magnetic field that temporarily changes its direction, the 2D Dirac electrons form a new localized state with a flat band dispersion, dubbed as a $\pi$-Landau level. Its wave function is a superposition of the clockwise and counterclockwise cyclotron orbits with time-periodic amplitudes, resulting in a novel closed trajectory shaped like a figure eight. Then, what would be the counterpart of the Hall effect in ac-magnetic fields? We find that a dc current in the transverse direction, i.e., a homodyne Hall current, is generated when an additional ac-electric field is applied. In the case of Dirac electrons, several electronic states contribute to this phenomenon including the $\pi$-Landau level. However, when the chemical potential $\mu$ is near the Dirac point, the dominant contribution comes from the low-energy electrons and we numerically find the homodyne Hall current to behave as $I_y=-\frac{e}{h}\mu$ per valley and spin. We explain this phenomenon through the high-frequency effective Floquet Hamiltonian which resembles the chiral Landau level Hamiltonian of three-dimensional Weyl Hamiltonian exhibiting chiral anomaly. We discuss the experimental feasibility and conclude that it is possible to realize this new exotic state using techniques such as THz metamaterial enhancement of magnetic fields.

The bulk and surface electronic structure of MoAlB(010) is studied by a combination of angle-resolved photoemission spectroscopy and density functional calculations. The observed bulk Fermi-level crossings agree with the previously reported bulk Fermi surface of the material. Additionally, we find several surface states in the wide projected bulk band gaps around the Fermi energy. The surface states differ in their stability under residual-gas exposure in the vacuum system and in the magnitude of their Rashba-type spin-orbit splitting. We explain this in terms of their elemental and orbital character. A surface state arising from Al dangling bonds is sensitive to surface contamination, whereas a mainly Mo-derived surface state exhibits the stronger spin-orbit splitting.

We present a finite-basis method for obtaining the one-electron Green's functions or wave functions in a general nonspherically symmetric, finite-range potential. The approach reformulates the problem in terms of a $T$ matrix with finite support, allowing the Green's functions or wave functions to be evaluated at real or complex energies. We consider the nonrelativistic limit and apply our method to several systems, showing that it reproduces analytic results in the spherically symmetric case and makes predictions for energy splittings as well as modified charge densities in the nonspherical case. The results demonstrate the capability, flexibility, and robustness of the $T$-matrix approach. Our method solves the long-standing problem of constructing numerically stable, nonspherical-potential Green's functions in multiple scattering theory and opens the door to applying this theory to warm dense matter.

Two-dimensional (2D) van der Waals materials are a promising platform for exciton state engineering. In this paper, we study the properties of excitons in 2D group VI transition metal dichalcogenide semiconductors that are modified by a periodic electrostatic potential through the quadratic Stark effect. Using a model that retains only center-of-mass and valley degrees of freedom, we find that electrostatic potentials can drive optical valley splitting up to $\sim 10\mathrm{meV}$ and induce valley-selective exciton dispersion. We explain why both properties are sensitive to the rotational symmetry of the electrostatic trapping potential using a combination of numerical results and analytical approximations. An important consequence of valley splitting is that the lowest exciton band is nondegenerate and has a linear dispersion around $\mathit{\gamma }$ that is expected to suppress thermal excitations, allowing true Bose condensation and superfluidity of excitons in two space dimensions.

We predict geometric magnetotransport oscillations in ballistic graphene specific for a ring-shape geometry. Using the Büttiker-Landauer formalism, we analytically obtain the local Hall and Nernst coefficients in the weak-field ballistic regime. These coefficients exhibit pronounced oscillations as functions of both the magnetic field and the angular positions of the measurement probes. The oscillations originate from the discrete set of skipping orbits that geometrically connect the contacts, with resonances occurring when the angular separation between contacts times the radius of the disk equals an integer number of cyclotron diameters. Unlike conventional quantum oscillations in conductivity, this effect is robust at room temperature and can dominate local thermoelectric signals. This geometric control of ballistic flow provides a platform for studying electron hydrodynamics and engineering phase-coherent devices, with potential applications in sensitive terahertz detectors and thermal management systems.

Magneto-optical (MO) effects like Kerr and Faraday rotations provide a direct probe of topological order in thin films of the magnetic topological insulator (TI) ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ (MBT). Motivated by recent experimental studies of spin-flip/flop transitions in MBT thin films, we investigate the interplay between interlayer spin configurations, topological order, and MO response in five septuple-layer (5-SL) MBT using first-principles calculations and a simplified coupled Dirac cone model. Our results reveal that, despite possessing a nonzero out-of-plane magnetization, 5-SL MBT thin films can be either $\mathcal{C}=+1$ TIs or $\mathcal{C}=0$ topologically trivial insulators depending on the relative spin orientations of the top and bottom SLs. We evaluate the Faraday and Kerr rotation angles using tight-binding models derived from ab initio calculations and by comparing our results with those of a simplified coupled Dirac cone model to clarify the macroscopic mechanisms underlying the MO response of spin-flip states. These theoretical findings highlight the tunability of topological and MO properties in MBT thin films and provide microscopic insight into the emergence of complex topological order in layered antiferromagnetic materials.

${\mathrm{MoOCl}}_2$ is a metallic, layered van der Waals material with a strong in-plane structural anisotropy. The reflectivity of a ${\mathrm{MoOCl}}_2$ single crystal has been determined in a wide spectral range from the infrared to the visible regime. This reflectivity is extremely anisotropic, reflecting the anisotropic crystal structure and electronic properties of ${\mathrm{MoOCl}}_2$. Using a Drude–Lorentz fit, we extracted the dielectric function quantitatively for the two in-plane directions of ${\mathrm{MoOCl}}_2$, and we determined the anisotropic optical effective mass of the conduction electrons. Our data additionally demonstrate the presence of interband excitations in the measured spectral range.

Tip-Enhanced Raman Spectroscopy (TERS) can be used to make nanoscale spatial measurements of 2D materials, such as graphene and transition metal dichalcogenides (TMDs). The TERS theory introduced in [Cançado et al., Phys. Rev. X 4, 031054 (2014)], however, was tailored for graphene, whose out-of-plane Raman response is neglected. In the present work, we include the out-of-plane response in the TERS theory. In doing so, we provide an exact analytical expression for the field propagation between the tip and the sample, and show that the contribution to the TERS signal that scatters first at the sample, then at the tip (sample-tip, or TS) is important only when the out-of-plane response is significant. We extensively study the variation of TERS experimental measurements when varying physical parameters of the system, like the tip radius, the out-of-plane response, the TERS coherence length, and others. It becomes evident that the TERS enhancement is very sensitive to the out-of-plane Raman response of the phonon mode, while normalized tip-approach measurements are more sensitive to the coherence length, and we show that the medium refractive index leads to an effective tip enhancement factor $f_e$. Our results lead to the conclusion that, in general, a strong TERS enhancement is a necessary condition for investigating the physics discussed here, which here means surveying the difference in TERS signals between different Raman modes. We use our model to analyze some graphene TERS experiments, showing that they are consistent with a negligible out-of-plane Raman response and a nonzero TERS coherence length in the fitting.

We investigate thermoelectric transport in monolayer graphene across a finite complex barrier within a Landauer scattering framework. Solving the Dirac–Weyl problem exactly, we show that the imaginary part of the barrier renders the scattering matrix nonunitary and replaces the usual Hermitian flux conservation by a generalized flux-balance relation determined by the net gain or loss inside the barrier. In the Hermitian limit, the standard graphene $n\text{−}p\text{−}n$ barrier behavior is recovered, including perfect transmission at normal incidence and Fabry–Perot-type resonances. For a finite imaginary part, however, the same resonant channels are selectively attenuated or amplified, which significantly modifies both the angular response and the conductance profile. We further show that the lead-resolved conductances become dependent on the bias partition, providing a direct signature of the breakdown of gauge invariance in the effective two-terminal response. At finite temperature, the exact linear-response coefficients reveal a clear trade-off controlled by the imaginary part of the barrier: gain enhances both the electrical and thermal conductances, whereas loss suppresses the thermal conductance more efficiently and yields the largest thermoelectric figure of merit within the parameter range considered. These results demonstrate that complex barriers extend the range of transport behaviors accessible in graphene beyond the usual Hermitian $n\text{−}p\text{−}n$ junction. They also suggest a practical interpretation of the imaginary potential as an effective reduced description of unresolved source–sink channels or additional probes coupled to the device, particularly when a fully microscopic model of the environment is not available.

Manipulating spin for quantum information and spintronic devices requires quantitative prediction of quantum transport over long time and length scales. We introduce a computational framework for first-principles density-matrix quantum transport within the Wigner function formalism that facilitates spin dynamics and transport simulations, while accounting for electron-phonon scattering at device length scales. This allows us to elucidate the impact of realistic spin-orbit fields, such as Rashba and persistent spin helix, on coherent spin transport in several materials, as well as the transition to incoherent transport with increasing strength of electron-phonon scattering. We identify three distinct regimes of incoherent spin transport corresponding to the free induction decay, Dyakonov-Perel, and Elliott-Yafet regimes of spin relaxation, and find a scattering-strength-independent spin diffusion length within the Dyakonov-Perel regime. With applied magnetic fields, spin transport in this regime is sensitive to scattering strength and leads to asymmetric Hanle curves that probe the internal spin-orbit field of the material.

We investigate the pressure-induced evolution of crystal structure and magnetism in the kagome ferromagnet ${\mathrm{Fe}}_3{\text{Sn}}_2$ by combining x-ray diffraction, x-ray emission spectroscopy, x-ray magnetic circular dichroism, and spin-polarized density functional theory calculations. X-ray diffraction reveals a structural phase transition above $\sim 20\mathrm{GPa}$, which coincides with a pronounced reduction of the local Fe magnetic moment evidenced by x-ray emission spectroscopy, indicating a high-spin to low-spin transition. While x-ray emission spectroscopy probes the amplitude of the local moment, XMCD provides direct information on the orientation of the ordered magnetic moments and uncovers a rich pressure–temperature magnetic phase diagram. At room temperature, a collinear ferromagnetic phase with moments aligned along the $c$ axis persists up to the structural transition. At low temperature, a tilted magnetic configuration remains stable to significantly higher pressures, while at intermediate temperatures pressure stabilizes the low-temperature magnetic phase at the expense of the high-temperature one. Spin-polarized first-principles calculations show that, although isotropic ferromagnetic exchange interactions remain robust under compression, pressure enhances spin-orbit-driven magnetic anisotropy and Dzyaloshinskii-Moriya interactions, favoring noncollinear magnetic configurations. Furthermore, hydrostatic pressure reconstructs the kagome-derived low-energy electronic structure, redistributes the Berry curvature in momentum space, and suppresses the intrinsic anomalous Hall conductivity despite the preservation of the metallic state. Our results demonstrate that pressure simultaneously reshapes the magnetic energy landscape of ${\mathrm{Fe}}_3{\text{Sn}}_2$ and Berry-phase electronic transport by coupling lattice, spin state, and relativistic magnetic interactions, establishing hydrostatic pressure as an effective control parameter to engineer magnetic anisotropy and electronic topological phases in kagome materials.

Disordered superconductors in low dimensions provide an exemplary manifestation for the role of quantum fluctuations in a many-body system. Specifically in Josephson arrays with comparable Josephson and charging energies ($E_J\sim E_C$), disorder tends to change the nature of the paradigmatic superconductor-insulator transition and potentially leads to formation of multiple distinct phases. We address this problem in a model of a two-legged Josephson ladder subjected to a wide spatial distribution of its parameters along the legs. In contrast, we assume the system to have a perfect ${\mathbb{Z}}_2$ symmetry to interchange between the legs, and investigate the effects of spatial randomness which preserves this symmetry in the strong-disorder limit. To this end, we apply a strong randomness real-space renormalization group technique and explore the resulting phase diagram. We identify three disorder-dominated phases, including an intermediate phase between a disordered superconductor and a disordered insulator. The latter insulating phase can be mapped to a XY spin chain in a spin-glass phase, while the intermediate phase turns out to be a Bose glass.

We consider the Bethe ansatz integrable Russian doll (RD) model of superconductivity with time-reversal symmetry breaking, which exhibits a cyclic renormalization group. By obtaining an exact solution for the renormalization group flows, we investigate the phase structure in the one-pair sector, which includes localized, fractal, and delocalized phases. We show that the quantum number $Q$, arising from the Bethe ansatz equations, counts the number of cycles and parametrizes the towers of states. Using the action of the renormalization group on the eigenstates, we demonstrate that $Q$ serves as an order parameter, providing a mechanism for the formation of the fractal phase in the deterministic systems and an example of the interplay between fractality and cyclic RG.