We present an approach to solving the ground state of Fermi systems that contain spin or other discrete degrees of freedom in addition to continuous coordinates. The approach combines a Markov chain Monte Carlo sampling for energy estimation that we adapted to cover the extended configuration space with a transformer-based wave function to represent fermionic states. A transformer with both continuous position and discrete spin as inputs achieves universal approximation to spinful generalized orbitals. We validate the method on a range of two-dimensional material problems: a two-dimensional electron gas with Rashba spin-orbit coupling, a noncollinear spin texture, and a quantum antiferromagnet in a honeycomb moiré potential.

Inspired by the recent experimental progress in pyrochlore derivative ${\mathit{R}}_3{\mathrm{Sb}}_3{\mathit{A}}_2{\mathrm{O}}_{14}$ $(R=\text{rare earth};$ $A=\mathrm{Mg}, \mathrm{Zn})$, we investigate the Hubbard model on the kagome lattice with an additional hopping $t^{\prime }/t$, which enables continuous interpolation between the kagome and triangular lattices by using determinant quantum Monte Carlo simulations. We find that increasing $t^{\prime }/t$ suppresses the nearest-neighbor antiferromagnetic correlations. Concurrently, the next-nearest-neighbor antiferromagnetic correlations are enhanced and closely associated with the emergence of a pronounced low-temperature peak in the specific heat. Increasing on-site interaction $U$ enhances magnetic correlations and shifts the associated $t^{\prime }/t$ crossover points to larger values. We also discuss the sign problem to clarify which parameter region of our numerical simulations is accessible and reliable. Our results uncover the competition between frustration and correlations and the interplay of magnetic and thermodynamic responses in the kagome lattice, providing insights into correlated states in frustrated materials.

Higher-order topological phases with invertible symmetries have been extensively studied in recent years, revealing gapless modes localized on boundaries of higher codimension. In this work, we extend the framework of higher-order symmetry-protected topological (SPT) phases to include noninvertible symmetries. We construct a concrete model of a second-order SPT phase in $2+1$ dimensions that hosts symmetry-protected corner modes protected by a noninvertible symmetry. This construction is then generalized to a $d\text{th}$-order SPT phase in $d+1$ dimensions, featuring similarly protected corner modes. Additionally, we demonstrate a second-order SPT phase in $3+1$ dimensions exhibiting hinge modes protected by a noninvertible symmetry.

As fundamental one-dimensional defects, screw dislocations profoundly reshape the energy landscape and carrier dynamics of crystalline materials. By restoring the exact algebra of the screw dislocation group, we unveil the latent symmetry constraints that govern the electronic structure, providing a more rigorous physical picture than the conventional treatments. When applied to GaN, the method yields a band-connectivity constraint and rigorous dipole selection rules for polarization-resolved transitions. Combined with the computed Hamiltonian matrix, the approach gives symmetry-filtered radiative and dielectric calculations and reveals a piezoelectrical effect at the dislocation core that strongly suppresses radiative recombination. The pronounced dominance of nonradiative capture over radiative recombination highlights the detrimental impact of screw dislocations on the luminous efficiency of GaN, providing a theoretical foundation for optimizing dislocation-limited optoelectronic devices.

The Langevin equation has been a workhorse for understanding the rate of bimolecular recombination in optoelectronic and photovoltaic materials for over a century. Countless experiments have shown that it overpredicts nongeminate radiative recombination, by as much by several orders of magnitude, prompting researchers to develop numerous correction factors that account for impacts of inhomogeneity in material composition, carrier concentration, and mobility. Here we show that the presence of free carriers leads to screening, which contributes to lowering the bimolecular recombination rate even in a homogeneous material. We develop an expression that captures carrier screening of the Coulomb attraction that leads to recombination. Our expression relates the recombination rate to the concentration of free carriers and to energetic disorder, which stems from the steepness of the density of states. We define a generalized Coulomb capture radius $r_0$, based on the energetic disorder $E_0$, as well as a screened capture radius $r_{\text{sc}}$, and then show that the recombination rate is reduced from the Langevin expression by a ratio $r_{\text{sc}}/r_0$, a significant reduction when carrier concentration is large and energetic disorder is low. We also show that the rate still factors into a term containing mobility and a term that is proportional to the $np$ product, now with a reduction due to screening, which reduces the order of this nominally quadratic bimolecular term below second order, as observed in experiments that separately quantify the contribution from mobility to the order. Our work establishes a stricter upper bound on the bimolecular recombination rate and points to materials properties that may result in higher efficiency across many future optoelectronics and photovoltaics.

We perform a differential resistance study in the hydrodynamic regime of an electron liquid in GaAs/AlGaAs quantum wells. At zero magnetic field $\left(B\right)$ a Lorentzian profile occurs in the nonlinear transport driven by a U-turn (ac) current loop, in $(\mathrm{ac}+\mathrm{dc})$ measurements a minimum deepens with the external dc current bias $\left(j_{\text{dc}}\right)$. Our analysis shows that the observed electronic transport valley induced by $j_{\text{dc}}$ is attributed to the Joule heating effect on the electron temperature $\left(T_e\right)$ of the electron liquid. Quantitatively, we demonstrate that the viscosity resistivity $\left(\mathrm{\Delta }\rho \right)$ is proportional to $T^{-2}$ and is consistent with the dc-current-induced electronic Gurzhi effect in various configurations of measurement.

Non-Abelian topological charges, characterized by their noncommutative algebra, offer a framework for describing multigap topological phases beyond conventional Abelian invariants. Although higher-order topological phases (HOTPs) host boundary states at corners or hinges, their characterization has largely relied on Abelian invariants such as winding and Chern numbers. Here, we propose a coupled-wire scheme for constructing non-Abelian HOTPs and analyze in detail a two-dimensional model as its minimal realization. The resulting Hamiltonian supports hybridized corner modes, protected by parity-time reversal $\left(\mathcal{PT}\right)$ plus sublattice symmetries, and described by a topological vector that unites a non-Abelian quaternion charge with an Abelian winding number. Corner states emerge only when both invariants are nontrivial, whereas weak topological edge states of non-Abelian origin arise when the quaternion charge is nontrivial, enriching the bulk-edge-corner correspondence. The system further exhibits topological phase transitions of both non-Abelian and Abelian characteristics, providing a unified platform that bridges these two distinct topological classes. Our work thus extends the study of HOTPs into non-Abelian regimes and suggests feasible experimental realizations in synthetic quantum matter.

We study Andreev-mediated transport and current fluctuations in interacting normal-superconducting quantum-dot systems. Using a generalized master equation based on real-time diagrammatics and full counting statistics, we compute the steady-state current, zero-frequency noise, and rate of entropy production in the large superconducting-gap limit. We show how Coulomb interactions modify Andreev-mediated transport by renormalizing resonant conditions and suppressing superconducting coherence, leading to a pronounced reduction of current precision even when average currents are only weakly affected. These effects are particularly evident at high temperatures, where conventional Coulomb-blockade features are thermally smeared while fluctuation properties remain highly sensitive. By analyzing thermodynamic uncertainty relations, we demonstrate that violations of the quantum bound present in the noninteracting regime are progressively reduced and eventually suppressed as interactions increase, whereas the recently proposed hybrid bound remains satisfied. Our results clarify how Coulomb interactions and nonequilibrium fluctuations jointly determine transport properties in hybrid superconducting devices, and establish current precision as a robust benchmark for interacting Andreev transport beyond the noninteracting limit.

We introduce a one-dimensional non-Hermitian Kitaev chain with staggered imbalance in the $p$-wave superconducting pairing. By tuning the chemical potential and the pairing imbalance, we find that the eigenenergy spectrum undergoes real-to-complex transitions, and the spectral gap can change from a real line gap to an imaginary one. The pairing imbalance significantly enlarges the parameter region supporting a topological superconducting phase. Remarkably, we show that a topologically nontrivial phase hosting Majorana zero modes can be induced by varying the pairing imbalance, even in the regime of strong chemical potential. The gap-closing points and phase boundaries are determined analytically, and the resulting phase diagrams are presented with the nontrivial phase characterized by a nonzero topological invariant. Furthermore, we identify the coexistence of Majorana zero modes and finite-energy Majorana edge modes in this system. Our results reveal exotic phenomena arising from imbalanced pairing and establish a platform for exploring topological superconductivity in non-Hermitian systems.

We propose a theoretical framework in which a one-dimensional (1D) tight-binding model incorporating unconventional magnetic order together with Rashba and Ising spin-orbit couplings are considered to realize two key phenomena in condensed matter systems: topological superconductivity and the superconducting diode effect (SDE). We first elucidate the underlying band topology of the normal-state Hamiltonian and subsequently introduce an on-site attractive Hubbard interaction. Performing a a self-consistent mean-field analysis, we establish superconducting order parameters in both the conventional Bardeen-Cooper-Schrieffer (BCS) and finite-momentum Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing channels. Intriguingly, both pairing states can support topological superconductivity, characterized by a nontrivial winding number, and lead to the emergence of four zero-energy Majorana modes localized at the ends of the 1D chain. The FFLO state further gives rise to an intrinsic field-free SDE, manifested as a nonreciprocal supercurrent and quantified by the diode efficiency $\eta$. Notably, our model yields a large diode efficiency $\eta \sim 65\%$, highlighting its potential for realizing topological superconductivity and highly efficient superconducting devices.

In this theoretical work, we propose an all-optical method for fast and precise manipulation of twist angle in two-dimensional multilayer by transferring orbital angular momentum from phase-structured light (e.g., vortex beams) to a 2D material flake. We model the light-matter interaction, analyze the twist dynamics, and develop a phase diagram for optical twists by mapping the system onto an impulsively forced nonlinear pendulum. Our findings reveal rich dynamical responses spanning single- and multipulse twist angle control to (quasi)stable dynamical trajectories, and suggest a pathway for all-optical measurement of the twist potential energy. Aided by classical potential estimates for the interlayer energy and numerical simulations, we demonstrate the feasibility of this approach with hexagonal boron nitride (hBN) bilayers and extend the results to transition metal dichalcogenides (TMDs) with first-principles calculations. These results can be generalized to other 2D multilayers, paving the way for customizable moiré electronics and photonics.

We present a numerical study of the two-dimensional quantum percolation model, revealing that a critical region with multifractal eigenstates mediates the transition from localized to delocalized states. By analyzing the mean level ratio and participation entropy, we identify two distinct transitions: a Berezinskii-Kosterlitz-Thouless (BKT) transition at the classical percolation threshold, separating the localized and critical phases, and a power-law-like transition at a larger concentration, marking the onset of full delocalization. The critical phase is characterized by multifractal eigenstates, as evidenced by the generalized fractal dimension and multifractal spectrum. We present a detailed discussion of the results for a spectral window $E/t=0.60\pm 0.05$. The analyses were repeated for energy windows centered at different values of $E/t$, and the results are displayed in the form of a phase diagram as a function of energy; the outcome highlights the robustness of both the multifractal phase and the BTK transition. Altogether, our results establish that in the marginal two-dimensional case, the Anderson impurity model and the quantum percolation model belong to different universality classes.

The study of many-body localized phases intrinsically links spectral properties with eigenstate characteristics: localized systems exhibit Poisson level statistics and area-law entanglement entropy, while ergodic systems display volume-law entanglement and follow random matrix theory predictions, including level repulsion. Here, we introduce the interacting Anderson Quantum Sun model, which significantly deviates from these conventional expectations. In addition to standard localized and ergodic phases, we identify a regime that exhibits volume-law entanglement coexisting with intermediate spectral statistics. We also identify another nonstandard regime marked by Poisson level statistics, subvolume entanglement growth, and rare-event-dominated correlations, indicative of emerging ergodic instabilities. These results highlight unconventional routes of ergodicity breaking and offer fresh perspectives on how Anderson localization may be destabilized.

Quasi-one-dimensional bismuth halides offer an exceptional platform for exploring diverse topological phases, yet the nature of the room-temperature topological phase transition in ${\mathrm{Bi}}_4{\mathrm{I}}_4$ remains unresolved. While theory predicts the high-temperature $\beta$ phase to be a strong topological insulator (TI), experiments observe a weak TI. Here we resolve this discrepancy by revealing the critical role of electron-phonon coupling. Using our ab initio scheme for phonon-induced band renormalization, we show that thermal phonons alone drive $\beta –{\mathrm{Bi}}_4{\mathrm{I}}_4$ from the strong TI predicted by static-lattice calculations to a weak TI at temperatures where $\beta –{\mathrm{Bi}}_4{\mathrm{I}}_4$ is stable, with calculated surface states in close agreement with experiments. We further reveal that high-energy states shape the low-energy topology in $\beta –{\mathrm{Bi}}_4{\mathrm{I}}_4$ via phonon-mediated processes. Our work establishes the critical role of electron-phonon coupling in driving the topological phase transition and provides a broadly applicable approach for predicting topological electronic structure at finite temperatures.

Relaxor ferroelectrics can be categorized into single-phase relaxors, reentrant relaxors, and polymorphic relaxors in terms of domain structure features. Among these, polymorphic relaxors with nanodomains in at least two different phases exhibit superior energy storage/electrocaloric properties compared with the other two types of relaxors. However, it has remained unclear how polymorphic relaxors form because of limitations in characterization techniques and, more importantly, a lack of theoretical models. In this work, we develop a phase-field model of polymorphic relaxors based on a perovskite-structured binary ferroelectric system with a cubic (C) to tetragonal (T) transition at one end and a C to rhombohedral (R) transition at the other, incorporating both the nanoscale compositional heterogeneity arising from the random distribution of substituted ions and the local electric fields generated by heterovalent ion substitution. Based on this model, we reproduce the domain structure features as well as the dielectric permittivity behavior and construct a complete phase diagram for polymorphic relaxors, all of which are consistent with experimental observations. Further analysis shows that composition near the morphotropic phase boundary (MPB) and strong local electric fields are the critical dual factors driving the formation of polymorphic relaxors. Once the two necessary conditions are not simultaneously satisfied, either single-phase relaxors or reentrant relaxors occur. This work unravels the origin of polymorphic relaxor formation by developing a phase-field model of polymorphic relaxors, which provides a theoretical foundation for the design of relaxors with enhanced performance.

We demonstrate a nonzero twist-angle stabilization mechanism in lattice-mismatched 2D heterobilayers, which results from the geometric alignment between the flake edges and the vectors determining the moiré pattern supercell. Using atomistic simulations of graphene flakes on hexagonal boron nitride, with diameters of up to $\sim 2500\AA$, we identify twist angles corresponding to global minima in the twist-angle dependence of the interlayer interaction energy at $\sim 0.{61}^{\circ }$ for armchair and $\sim 1.{89}^{\circ }$ for zigzag-edged flakes, tunable via in-plane strain. This locking mechanism, which relies on energy barriers that are an order of magnitude larger than those of nearby metastable twist angles, provides a geometric route to precision twist-angle control of two-dimensional heterostructures and to understand the self-orientation of macroscopic flakes.

We study the low-energy excitation spectra of a spin-1/2 quantum Heisenberg model with a monoaxial Dzyaloshinskii-Moriya interaction. Using the density matrix renormalization group method, our analysis reveals a degeneracy between skyrmion and antiskyrmion states, enabling the formation of a Schrödinger cat state, a quantum superposition of these topologically distinct textures. To characterize this nontrivial state, we compute two-point spin correlation functions, highlighting signatures accessible via neutron scattering experiments. Furthermore, we demonstrate that applying a magnetic field gradient induces a coherent time evolution of the cat state, offering a controllable mechanism for its manipulation. These findings provide a framework for the detection of skyrmionic Schrödinger cat states in quantum magnets.

We perform nanosecond-resolution multiplexed readout on six same-chip superconducting microwave resonators. This allows us to pinpoint the position of ionizing radiation impacts on the chip by measuring the differential time-of-flight of the generated phonons, inducing correlated errors in the device, thereby implementing an on-chip seismic array. We correlate the phase response of each resonator—a proxy for the absorbed energy—to the distance from the impact point to uncover a millimetric characteristic length for the phonon-mediated radiation poisoning.