We present a fully quantum-mechanical study of the energy-momentum dispersion of running waves, spin-conserving neutral excitations, and spin-reversal neutral excitations in a spin-polarized two-dimensional (2D) Wigner crystal. Our results show that the collective modes—plasmon and transverse sound—closely follow classical predictions even at surprisingly low values of $r_s\sim 8$. Furthermore, by extracting the shear modulus from the transverse sound speed, we find that quantum-mechanical effects enhance the shear modulus at high densities, leading to a (Kosterlitz-Thouless-Halperin-Nelson-Young) melting temperature that exceeds the classical prediction. In addition, we apply the quasiboson approximation to compute the correlation energy of the 2D WC based on its neutral excitation spectrum. While this approach underestimates the absolute correlation energy compared to quantum Monte Carlo results, it successfully captures the overall trend. We further investigate the stability of the metallic Wigner crystal, a partially melted crystalline state that retains a Fermi surface, and find that it is unstable toward density fluctuations, with the instability concentrated at wave vectors set by the Fermi pocket size. These findings establish a robust quantum-mechanical foundation for understanding elementary excitations in Wigner crystals within low-dimensional electron systems and provide valuable theoretical insights for future experimental studies.

Traditional theories of electron transport in crystals are based on the Boltzmann equation and do not capture physics arising from quantum coherence. We introduce a transport formalism based on orbital Wigner functions, which accurately captures quantum coherent physics in multiband fermionic systems. We illustrate the power of this approach compared with traditional semiclassical transport theory by testing it numerically against microscopic simulations of one-dimensional, noninteracting, two-band systems—the simplest systems capable of exhibiting interorbital coherence. We show that orbital Wigner functions accurately capture strongly nonequilibrium features of electron dynamics that lie beyond conventional Boltzmann theory, such as the ballistic transport of a relative phase between microscopic orbitals and topological Thouless pumping of charge, both at nonzero temperature and away from the adiabatic limit. Our approach is motivated in part by modern ultracold atom experiments that can prepare and measure far-from-equilibrium charge transport and phase coherence in multiband fermionic systems, calling for correspondingly precise theories of transport. The quantitative accuracy exhibited by our approach, together with its capacity to capture nontrivial physics even at the ballistic scale, establishes orbital Wigner functions as an ideal starting point for developing a fully systematic theory of transport in crystals.

We investigate equilibrium charge transport in a finite mesoscopic ring with nearest-neighbor Rashba spin-orbit coupling (SOC) and on-site Hubbard interactions. Using a self-consistent Hartree-Fock (HF) Green's-function approach, we compute persistent currents and the Drude weight while varying the Aharonov-Bohm flux $(\varphi /{\varphi }_0)$, Rashba strength ${\lambda }_R$, Hubbard interaction $U$, and electron filling. Within this finite-ring HF description, the transport response is governed by the competition between flux-sensitive single-particle dispersion, SOC-induced level rearrangements, and interaction-induced suppression of charge motion. Increasing $U$ monotonically reduces the Drude weight over the parameter range explored, consistent with a progressive reduction of flux sensitivity in the occupied HF spectrum. By contrast, Rashba SOC does not produce a simple monotonic enhancement. Instead, $D\left({\lambda }_R\right)$ is strongly nonmonotonic: at selected values of ${\lambda }_R$, SOC brings levels near the chemical potential into near-degeneracy or avoided crossings, producing pronounced resonant enhancements of the flux curvature, whereas at other values the response can be lower than in the ${\lambda }_R=0$ case. For the even-$N$ nearest-neighbor ring considered here, particle-hole symmetry relates fillings $N_e$ and $2N-N_e$. In the symmetry-preserving HF solution, the corresponding Drude weights and persistent-current profiles agree within numerical tolerance. In the finite $N=8$ ring, the largest Drude weight in the explored parameter window occurs at half filling. This result should be understood as a finite-size HF charge-stiffness effect, not as a statement about the exact thermodynamic Mott limit of the one-dimensional Hubbard model. Overall, the results provide a controlled mean-field picture of how Rashba SOC and Hubbard interactions compete in flux-sensitive mesoscopic transport and they identify tunable SOC regimes where the charge stiffness can be strongly enhanced.

Using the full-band $\mathbf{k}·\mathbf{p}$ Hamiltonian model and the lattice Green's function method combined with the Landauer-Büttiker formula, we investigate the magnetotransport and magnetic-field-dependent electronic structure in monolayer InSe and its nanoribbons. Landau levels of the topmost valence band of the monolayer InSe first vary linearly and then quadratically with increasing magnetic field strength. Interestingly, four edge electronic states emerge for each Landau level as the monolayer InSe is confined to nanoribbons. However, this unusual Landau level will evolve into a conventional one with increasing magnetic field strength, which has two edge electronic states. The evolution of Landau levels with increasing magnetic field strength gives rise to a step transition from $4Q_0$ to $Q_0$ in the charge conductance of the two-terminal InSe nanoribbon. Here $Q_0=2e^2/h$ is the charge conductance quantum, where $h$ is the Planck's constant and $e$ is the elementary charge. Moreover, the intrinsic conducting electronic states in the InSe nanoribbon with a perpendicular magnetic field are verified by analyzing disorder effects and the six-terminal Hall and longitudinal resistance characteristics. Both bulk and edge electronic states contribute to transport as the magnetic field strength is relatively small, whereas only edge electronic states conduct as the field is increased. Meanwhile, a step transition of the Landau level filling factor from 4 to 1 is found as well. These findings provide a deeper understanding of the magnetoelectronic structures and magnetotransport features of electronic systems with Mexican-hat-like dispersion.

In Damerow and Kehrein [Phys. Rev. B 113, 165102 (2026)] proposed the conjecture that, for quantum quenches within the same phase, the overlap between the initial ground state and postquench eigenstates is maximal for the postquench ground state. We show that this statement is not valid in general. An explicit local, translationally invariant, gapped free-fermion counterexample exists even though the pre- and postquench Hamiltonians are connected by a symmetry-preserving gapped path and the thermodynamic-limit spectrum is continuous. The example therefore indicates that phase equivalence must be supplemented by an additional dynamical or geometric condition, beyond the absence of an equilibrium phase boundary.

The non-Hermitian skin effect is a nonreciprocity-induced localization phenomenon in which a macroscopic number of eigenstates accumulate anomalously at the boundary, accompanied by the extreme sensitivity to boundary conditions. Here, we develop a geometric characterization of the non-Hermitian skin effect. We demonstrate that the localization length scale associated with the skin effect is encoded in the quantum metric defined solely from right eigenstates, but not in the biorthogonal quantum metric. Moreover, we show that quantum metrics can exhibit power-law divergences at gapless points that depend on different boundary conditions. We also reveal that cusps of the generalized Brillouin zone in non-Bloch band theory are signaled by discontinuities in the quantum metrics. We illustrate these behaviors using prototypical non-Hermitian models, such as the Hatano-Nelson model and the non-Hermitian, nonreciprocal Su-Schrieffer-Heeger model.

We introduce a geometrical framework to construct a large class of time-dependent quantum systems in which the position of a classical particle moving autonomously on a smooth connected manifold is used to steer a quantum Hamiltonian over time. This results in quantum drives with structured temporal profiles and properties dependent on the local and global nature of the underlying choice of manifold. We show that our construction recovers the well-known classes of periodically driven and quasiperiodically driven quantum systems, but also unveils fundamentally new classes of quantum dynamics: by utilizing a compact two-dimensional hyperbolic Bolza surface and a nonorientable Klein-bottle surface, we demonstrate examples of a hyperbolically driven quantum system and a nonorientably driven quantum system respectively. Furthermore, we demonstrate that these driven systems exhibit unusual quantized dynamical responses reflecting their different underlying topologies, under the condition of being fully gapped and in the adiabatic limit, and which have interpretations as quantized crystalline electromagnetic responses in certain exotic effective tight-binding lattice models. We envision geometric quantum driving as a general framework to chart the landscape of time-dependent quantum systems and investigate the universal phase structures they exhibit, as well as a useful tool to enhance the capabilities of modern day quantum simulators.

Severe nonradiative recombination loss occurs in ${\mathrm{Cu}}_2{\mathrm{ZnSnS}}_4$-based solar cells, which is related to the prevalent Cu-Zn cation disorder and the deep defect states. However, due to the inherent complexity of site-dependent defect energetics in disordered systems, the synergistic mechanism between these crucial defects remains elusive. Using rigorous first-principles calculations, we demonstrate that the prevalent cation disorder markedly enhances defect-assisted nonradiative carrier capture, increasing the capture coefficient by approximately 2 orders of magnitude compared to the ordered lattice. We show that cation disorder affects the nonradiative capture primarily by altering the transition energy through band fluctuations, softening the lattice, and amplifying the lattice relaxations during the defect charge-state transitions. Notably, we find that the lattice softening can suppress the nonradiative capture, whereas its effect is surpassed by the transition energy and lattice relaxations that have even stronger effects on promoting the capture. This work elucidates the impacts of cation disorder on defect-assisted nonradiative capture, and the mechanism presented here is crucial for defect characterization and efficiency improvement of kesterite-based photovoltaic devices.

We solve numerically exactly a simple toy model to quantum general relativity or more properly to path integral on a curved space. We consider the thermal equilibrium of a quantum many-body problem on the sphere, the surface of constant positive curvature. We use path integral Monte Carlo to measure the kinetic energy, the internal energy, and the static structure of a bosons, fermions, and anyons fluid at low temperatures on the sphere. For bosons we also measure the superfluid fraction and compare its behavior at the critical temperature with the universal jump predicted by Nelson and Kosterlitz in flat space in the thermodynamic limit at the superfluid phase transition. For fermions and anyons it is necessary to use the restricted path integral recipe to overcome the sign problem. Even if this recipe is exact for the noninteracting fluid it reduces to just an approximation for an interacting system. And we make the example of the electron gas at low temperature. Snapshots of the many-body path configuration during the evolution of the computer experiment show that the “speed” of the single-particle path near the poles slows down as a consequence of the “hairy ball theorem” of Poincaré. The influence of curvature on the thermodynamic and structural properties of the many-body fluid is also studied.

Polaritons in van der Waals materials produce an enhanced light-matter interaction that enables a vast range of applications including single-photon sources, nanolasers, and nanosensors. However, achieving customized polariton excitation across a broad spectral range within a single intrinsic platform remains challenging. Here we identify a family of two-dimensional honeycomb boron allotropes that intrinsically support spectrally customized plasmon polaritons over a wide frequency range. First-principles calculations reveal Dirac dispersions at the K point in all allotropes, with one phase hosting a Dirac cone pinned to the Fermi level. Variations in band curvature near the Fermi energy modify the carrier effective mass and interband optical transitions, thereby shifting the plasma frequency and reshaping the dielectric response. This electronic tunability directly controls the polariton dispersion and enables distinct spectral regimes within the same material system. The resulting modes exhibit low dissipative losses and long propagation lengths that surpass those of conventional noble metals such as Ag and Au. These results establish two-dimensional boron as an intrinsic platform for broadband, low-loss, and spectrally programmable polaritons.

Based on the extended Bogoliubov–de Gennes theory, we investigate topological defect states in a time-reversal symmetry-breaking $s+id$ superconductor. In a square lattice hosting two single-quantum vortices along the diagonal, temperature, and intrinsic parameters can drive the splitting of composite vortices into fractional (anti)vortices, giving rise to bow-tie-shaped solitons and skyrmionic chains as well as coreless-type topological excitations. Interestingly, a suitably chosen nonmagnetic impurity near a vortex core induces a skyrmion texture by selectively trapping one single-component vortex, while a magnetic impurity always retains composite vortex structures. In the absence of spin-orbit coupling, the system responds isotropically to Zeeman fields, exhibiting a universal critical field for skyrmion formation. Once spin-orbit interaction is introduced, this response becomes highly anisotropic, with both the critical field strength and the spatial orientation of the resulting skyrmions depending sensitively on the field direction. The simultaneous presence of Rashba and Dresselhaus couplings further reduces the symmetry of the spin-split Fermi surfaces and enables a purely spin-orbit-driven vortex-to-skyrmion transition. In the strong Rashba regime, the system enters a second-order topological superconducting phase, where vortex matter undergoes profound reconstruction as the chemical potential varies. The skyrmion structure emerges at appropriate doping levels, and unique topological defect configurations with fragmented vortex cores are produced upon approaching half filling.

Experimental observations on ${\mathrm{KTaO}}_3$ superconductivity report widely different critical temperatures with a clear hierarchy among different crystallographic orientations. Accounting for spatial confinement, we connect the inhomogeneous superconducting order parameter with the spatial extent of the two-dimensional electron gas. We reproduce the observed hierarchy within a unified framework, based on a self-consistent tight-binding slab model with local spin-singlet $s$-wave pairing. The methods developed here can be readily extended to include more general interaction models, while still consistently including the characteristic spatial structure of the electron gas.

Under compression, elemental scandium (Sc) exhibits a remarkable monotonic increase in superconducting critical temperature ($T_c$), at a pressure of 240 GPa, reaching up to 37.6 K—the highest $T_c$ reported for all elemental solids to date. However, its electronic origin underlying this enhancement has remained elusive. Here, by combining first-principles calculations with an analysis of existing superconducting data, we elucidate the electronic mechanism driving pressure-enhanced superconductivity in the crystal structure Sc-III, Sc-IV, and Sc-V. Our in-depth analysis reveals that the increase in $T_c$ is intrinsically governed by progressive $d$-band broadening. Contrary to the conventional view of localized $d$ electrons, extreme pressure induces a substantial interatomic $3d\text{−}3d$ orbital overlap. By evaluating the Kohn-Sham potential barrier, we demonstrate that compression drives the $3d$ electrons to exhibit electronic behaviors analogous to those of $s$ and $p$ electrons toward a nearly free-electron regime, which naturally explains the strong electron-phonon coupling responsible for the rising $T_c$. Our work establishes a direct electronic descriptor for superconductivity in compressed Sc and provides a general framework for understanding pressure-induced phenomena in $d$-block metals.

Nonlinear Hall responses provide an electrical probe of Berry-curvature dipoles, but they are symmetry forbidden in many pristine two-dimensional metals. We show that layer-selective magnetic proximity provides a symmetry-controlled route to induce and tune anomalous and nonlinear Hall responses in metallic monolayer $1H\text{−}\mathrm{Nb}{X}_2$ ($X=\mathrm{S},\mathrm{Se},\mathrm{Te}$), where the nonmagnetic $D_{3h}$ crystal has vanishing anomalous Hall conductivity and a Berry-curvature dipole. Fully relativistic density-functional theory combined with Wannier interpolation shows that an out-of-plane proximity exchange preserving $C_3$ generates a sizable sheet anomalous Hall conductivity, ${\sigma }_{xy}^{\mathrm{sheet}}\sim {10}^{-2}(e^2/h)$ in representative active windows, while the Berry-curvature dipole remains zero. Breaking $C_3$ by introducing an in-plane exchange component, or by using an orthogonal two-sided exchange texture, produces a tunable Berry-curvature dipole and hence a nonlinear Hall response. Its exchange-odd part is linear in the in-plane exchange to leading order in the minimal model; the calculated spectra reach and can exceed $|D_y|\sim {10}^{-2}\AA$, with the largest and sharpest features in ${\mathrm{NbTe}}_2$. These trends are rationalized by symmetry analysis and an interface-induced $k$-linear Rashba-Zeeman minimal model. Within the idealized proximity model, an orthogonal dual-interface geometry further provides component-selective sign reversal of the first- and second-harmonic Hall signals in the same Hall-bar configuration.

We theoretically study direct current generation in a quantum spin chain induced by spinon excitations by light irradiation. We consider a $S=1/2$ one-dimensional (1D) antiferromagnetic XXZ model with magnetoelectric coupling that describes multiferroics with broken inversion symmetry. We perform the real-time simulation using infinite time-evolving block decimation, and demonstrate the direct current generation under light irradiation. By comparing the second-order nonlinear conductivity and the two-spinon excitation spectra of a 1D XXZ model, we confirm that the spinon excitations are the origin for the direct current generation in the quantum spin chain. We find that the bulk photovoltaic effect is driven by electric polarization carried by the spinons through the shift current mechanism, and thus is regarded as “the spinon shift current.”