We study the effects of a transverse magnetic field on the $J_1\text{−}{J}_2\text{−}{J}_3$ Ising model on the honeycomb lattice. By employing the cluster mean-field method, we investigate the nature of classical and quantum phase transitions, entropy accumulation, and the Grüneisen parameter focusing in the case with ferromagnetic first-neighbor interactions ($J_1>0$) and antiferromagnetic third-neigbor interactions ($J_3<0$). This frustrated model exhibits a competition between the zigzag (ZZ) antiferromagnetic and ferromagnetic (FE) phases that can be controlled by tuning $g_2=J_2/J_1$. Our findings indicate only continuous phase transitions between FE and paramagnetic (PM) phases in both classical and quantum limits. On the other hand, the ZZ-PM phase boundary can exhibit both classical and quantum tricriticality, with first-order phase transitions appearing near the regime of strong competition between FE and ZZ phases. We also find that increasing the transverse magnetic field can transform classical first-order transitions into continuous phase transitions across the ZZ-PM phase boundary, introducing a tricritical point in the field-temperature phase diagram. We map a wide range of competing interactions over which this phenomenon, called quantum annealed criticality, emerges through the interplay of classical and quantum fluctuations. Furthermore, entropy accumulation and a pronounced inverse magnetocaloric effect occur close to the quantum critical point and are particularly enhanced in scenarios where quantum annealed criticality is present. The relevance of our results to magnetic van der Waals materials exhibiting Ising anisotropy is also discussed.

We theoretically investigate the anomalous and diode Josephson effects in planar two-dimensional Josephson junctions with arbitrarily oriented exchange fields in two ferromagnets within the barrier, and spin-orbit coupling at the superconductor/ferromagnet interfaces, where the superconducting electrodes can have $s$-wave or arbitrarily oriented $d$-wave order parameter lobes. We perform a systematic symmetry analysis of the junction Hamiltonian and identify the minimal conditions for breaking time-reversal and space-inversion symmetries, which are required for the emergence of anomalous and diode Josephson effects. We classify the junctions into three classes for equal Rashba SOC at the two S/F interfaces, with particular attention to those between $d_{x^2-y^2}$ and $d_{xy}$ oriented superconductors. Our symmetry analysis is supported by numerical calculations of the current-phase relation (CPR) obtained using a generalized Furusaki–Tsukada (F-T) approach. By tuning the directions of the exchange fields in the ferromagnets, Rashba SOC at the interfaces, and superconducting order parameter orientations, nonreciprocity can be enhanced by more than 40%. We further analyze the phase-dependent Andreev bound states (ABSs) spectrum and their contribution to charge transport, as well as their signatures in the nonreciprocal transport characteristics. By comparing the current carried by ABSs with that obtained using the F-T technique, we find that the contribution from continuum states above the gap becomes pronounced in the presence of zero-energy crossings in the ABS spectrum and in junctions with $d$-wave superconducting electrodes because of the narrower superconducting gap, which may become closed. In the nonreciprocal regime, the ABS spectra show an asymmetric profile with respect to phase inversion, indicating the presence of a finite current at zero phase difference and unequal critical currents in opposite directions. Our results establish symmetry-based criteria and a microscopic mechanism for engineering nonreciprocal Josephson transport in hybrid superconducting structures.

The standard mean-field treatment of low-temperature superconductors leads to a square-root divergent density of states at the gap value. This feature can lead to unphysical logarithmic divergences in various quantities, such as currents and qubit transition rates. We revisit their possible regularization based on the proximity effect between two superconducting films with different gaps. We derive analytical approximations for the density of states in each superconducting film. We find that the smearing of the density of states grows with the gap asymmetry. As a concrete example, we discuss the regularization of transition rates in qubits with frequency close to resonance with the gap asymmetry between the two films, and the consequent smoothening of the jump discontinuity in the qubit frequency shift. Our results could also aid the development of superconducting detectors and related devices based on superconducting bilayers.

Polar topological textures in ferroelectrics can host internal structure beyond a single integer topological charge. Here, effective-Hamiltonian molecular-dynamics simulations are used to examine whether such internal fractional topology can be reconfigured by local electric excitation in ordered 12.5% Zr-substituted barium titanate. Chemical doubling along the polar axis stabilizes a coupled nanodomain texture consisting of alternating $\mathrm{Q}=-2$ antiskyrmionic and $\mathrm{Q}=+4$ skyrmionic slices, in which the local topological charge fragments into six −1/3 and six +2/3 localized contributions, denoted here as topological quarks, separated by Bloch-point-like singular conversion regions. Picosecond local electric-field pulses applied to selected vortex-core columns drive reconfiguration of the internal dipolar texture of a 2.6 nm nanodomain. Under a binary pulse-mask protocol addressing the six vortex cores, all 64 masks lead, within the chosen low-temperature simulation protocol, to distinct relaxed metastable configurations. The switching calculations are performed in a cryogenic regime, and the programmed states remain stable over at least 1 ns of field-free evolution on the simulation timescale. The resulting configurations are distinguishable both by sector-resolved topological fingerprints and by their real-space polarization fields. These results provide a computational proof of concept that fractional polar topology in a ferroelectric nanodomain can be locally reconfigured by ultrafast electric excitation and used as a multistate configurational degree of freedom in an idealized low-temperature setting.

An equation-of-state (EOS)-based construction of the Grüneisen function is developed and assessed through predictions of finite-temperature bulk moduli. In this approach, the volume dependence of the Grüneisen function is expressed analytically in terms of static EOS information, anchored by Debye temperatures obtained from elastic data sampled near equilibrium, and constrained by the infinite-compression limit. The resulting form requires as material-specific input only static energy-volume data and near-equilibrium elastic properties, with no parameters adjusted to thermal data. Within a Mie-Grüneisen-Debye framework, the approach is examined for diamond, magnesium oxide, silicon, and sodium chloride, chosen to span a broad range of stiffness, using machine-learning interatomic potentials from the Universal Models for Atoms (UMA) and Universal Point Edge Transformer (UPET) families, together with a dispersion-corrected variant of UMA. The calculated bulk moduli reproduce the expected experimental softening trends and capture the overall scale of the bulk-modulus temperature derivatives, although the level of quantitative agreement depends on the material, the underlying interatomic potential, and the selected analytic EOS form. These results show that an EOS-based construction of the Grüneisen function can capture the leading thermal-softening behavior of bulk moduli without fitting to thermal data. The observed sensitivity to the underlying static description further suggests that the framework may help identify deficiencies relevant to thermoelastic transferability and thereby inform future training and validation strategies for universal machine-learning interatomic potentials.

We study fractional topological numbers in open quantum systems described by the Gorini-Kossakowski-Sudarshan-Lindblad master equation. Under symmetry conditions ensuring quantization, we show that single-valued physical states in momentum space give rise to integer winding numbers that remain integer during time evolution. Fractional values arise when this condition is effectively relaxed, such that the topology is evaluated over a restricted sector or exhibits an effective multibranch structure. In these cases, the winding number is not quantized over the fundamental Brillouin zone and can depend continuously on system parameters, with discontinuities at purity-gap closings. However, when extended over multiple momentum periods, the winding recovers integer quantization. These effects are illustrated in a Su-Schrieffer-Heeger chain with gain and loss and can be probed in long-range hopping photonic lattices with fractional fillings via Bloch state tomography. Our results provide a unified framework for understanding fractional topology in open quantum systems.

In many metals, thermal transport is often dominated by electrons, although the lattice contribution can remain appreciable depending on the material. Here, through rigorous first-principles calculations, we uncover a phonon-dominated thermal transport regime in the Weyl semimetals TaAs and TaP. Remarkably, despite its metallic character, TaP exhibits an exceptionally high phonon thermal conductivity (${\kappa }_{\mathrm{ph}}$) of $162\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$ at room temperature, surpassing its electronic counterpart by nearly an order of magnitude. This anomalously high ${\kappa }_{\mathrm{ph}}$ arises from the combined effects of Weyl electronic structure, acoustic phonon bunching, and a large low-frequency–high-frequency phonon gap, which together suppress phonon-electron and three-phonon scattering. The linearly dispersing bands near the Fermi level yield a low electronic density of states, limiting both electrical conductivity and electronic thermal transport in these compounds. By further surveying a broad range of topological semimetals, we show that the prominence of phonon thermal transport is a universal characteristic of this material class. Our work provides deeper insight into thermal transport mechanisms in topological semimetals and broadens the scope for discovering metals with high thermal conductivity.

Altermagnets are collinear magnetically ordered states that exhibit momentum-dependent spin splitting in the absence of net magnetization and spin-orbit coupling (SOC). Related spin-splitting patterns, however, can also emerge in noncollinear magnetic systems with large SOC. Here we show, via a microscopic model, that the all-in-all-out (AIAO) state in pyrochlore iridates constitutes a noncollinear counterpart of a $d$-wave altermagnet stabilized by strong SOC. Starting from a microscopic $j_{\mathrm{eff}}=\frac{1}{2}$ tight-binding model on the pyrochlore lattice, we demonstrate that electronic interactions favor the AIAO phase and analyze its symmetry properties. We show that the AIAO order parameter transforms as an $A_{2g}^{-}$ octupolar magnetic moment, breaking time-reversal symmetry while preserving inversion and zero net magnetization. Using group-theory analysis and mean-field calculations, we demonstrate that this symmetry enforces both a spin-polarized momentum-dependent lifting of band degeneracies that is similar to that of a collinear $d$-wave cubic altermagnet, but also a band splitting at zero momentum. We show that the latter feature is captured by a low-energy model similar to the Luttinger-Kohn model for cubic semiconductors. Our results identify pyrochlore iridates as a platform for noncollinear counterparts of altermagnetism and provide a general symmetry framework for spin-split phenomena in spin-orbit coupled materials.

Magnetism in rare-earth intermetallics is generally governed by the coupled evolution of $4f$ spin and orbital moments, which typically diminish together once long-range magnetic order vanishes. Here we show that PrGaSi provides a clear exception to this paradigm. The Pr-$4f$ orbital magnetic moment does not collapse with the spin moment; instead, x-ray magnetic circular dichroism measurements show that it remains robust and even increases in the paramagnetic regime. Such behavior reflects the strong localization of the $4f$ orbital moment, which recovers its intrinsic $4f^2$ character once spin order–induced quenching is lifted. PrGaSi is a noncentrosymmetric ternary compound in which Weyl-type itinerant electronic states are expected to emerge, and first-principles calculations reveal that these linear-dispersive carriers persist across spin-ordered and spin-disordered phases. Their robustness is intimately linked to a coherent, momentum-locked channel that coexists with long-range, anisotropic Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions between localized Pr-$4f$ moments. Critical-scaling analysis provides evidence for long-range exchange interactions consistent with an RKKY-type mechanism associated with these itinerant electronic states. Furthermore, systematic magnetotransport measurements reveal an M-shaped magnetoresistance and low-temperature Hall anomalies, providing macroscopic evidence of the topological electronic responses coupled to this configuration. Together with the persistence of Weyl-type electronic features, the unusual decoupling between orbital strength and spin order positions PrGaSi as an unconventional magnetic system where localized orbital physics and itinerant topology remain intertwined across temperature regimes. These results highlight a scenario in which RKKY exchange coexists with Weyl-type itinerant electronic states, revealing a previously unexplored route for stabilizing orbital-anchored magnetism and for tuning magnetic anisotropy and topological responses in rare-earth systems.

We present a theoretical study of nonreciprocal charge transport in two-dimensional noncentrosymmetric superconductors, taking the transition-metal dichalcogenide ${\mathrm{MoS}}_2$ as a representative example. In the normal state, the magnetochiral anisotropy vanishes within the minimal band model of ${\mathrm{MoS}}_2$, appearing only at subleading order in the symmetry-breaking perturbations set by trigonal warping, Ising spin-orbit coupling, and the Zeeman field. Superconductivity changes this picture qualitatively: in the vicinity of the transition, the magnetochiral anisotropy is strongly enhanced by pairing fluctuations. We evaluate the nonreciprocal current density arising from order-parameter fluctuations and quantum-interference processes—the Aslamazov-Larkin and Maki-Thompson channels—and show that both are governed by cubic Lifshitz invariants of the Ginzburg-Landau free energy, generically allowed once inversion and time-reversal symmetries are broken. These invariants are derived microscopically from the band model, including the effects of disorder: in the diffusive limit, the warping-induced invariant is suppressed, yet the resulting response remains sizable. Strain is shown to enable additional vector components of the nonlinear current, activating the Maki-Thompson channel. Finally, invoking Onsager reciprocity, we identify kinetic Lifshitz invariants, nonreciprocal corrections to the order-parameter relaxation rate, locked to the Langevin noise by the fluctuation-dissipation theorem, and demonstrate that their contribution to the magnetochiral anisotropy is parametrically subleading near the transition.

We investigate the evolution of electronic transport across the topological insulator to trivial band insulator quantum phase transition in ${\mathrm{In}}_x{\left({\mathrm{Bi}}_{0.3}{\mathrm{Sb}}_{0.7}\right)}_{2-x}{\mathrm{Te}}_3$ thin films by tuning the indium concentration $x$, which systematically reduces the effective spin-orbit coupling. The observed transport evolution is consistent with a topological-to-trivial phase transition near $x\sim 7\%-10\%$, while a crossover from diffusive transport to a strongly localized Anderson insulating regime occurs around $x\sim 15\%$. In the diffusive regime, the magnetoconductance is well described by the Hikami-Larkin-Nagaoka formalism, with the evolution of the weak antilocalization prefactor $\alpha$ providing a transport signature consistent with the proposed topological-to-trivial phase transition. Beyond the diffusive limit, transport crosses into a variable range hopping regime, accompanied by a striking reversal of low-field magnetoconductance from negative to positive. The observed positive magnetoconductance, its pronounced anisotropy, and its temperature evolution point to an orbital origin of the response. These features are naturally captured by incorporating the incoherent hopping mechanism of Raikh et al. [Phys. Rev. B 45, 6015 (1992)] together with wave-function shrinkage, rather than through conventional quantum correction frameworks. Theoretical analysis based on first principles electronic structure calculations shows that increasing indium substitution suppresses the band inversion through the combined effects of indium-derived states and reduced spin-orbit coupling, supporting the interpretation of the observed transport evolution. Our results provide a unified picture of how topology, spin-orbit coupling, and disorder collectively describe the full field-temperature magnetotransport landscape in this material class.

Exact results for spin and charge transport in the Hubbard model on bipartite lattices with $N_a\gg 1$ sites and arbitrary spatial dimension $d$ are obtained using a recently introduced representation in terms of physical spins and physical $\eta$-spins. This includes results on the role played in spin and charge transport by the $\tau$-translational U(1) symmetry beyond SO(4), within the model's global $\left[\mathrm{SO}\right(4)\times \mathrm{U}(1)]/{\mathbb{Z}}_2$ symmetry. The $N_{s,\pm 1/2}=(N_a/2-S_{\tau }\pm S_s^z)$ physical spins with projection $\pm 1/2$ and the $N_{\eta ,\pm 1/2}=(2S_{\tau }\pm S_{\eta }^z)$ $\eta$-spins with projection $\pm 1/2$ that populate the energy and momentum eigenstates of the Hubbard model on bipartite lattices, where $S_{\tau }$ denotes the eigenvalue of the generator of the $\tau$-translational U(1) symmetry, are found to carry elementary spin $(\alpha =s)$ and charge $(\alpha =\eta )$ currents ${\vec{j}}_{\alpha ,\pm 1/2}=\pm {\vec{C}}_{\alpha }/N_{\alpha }$. Here, $N_{\alpha }=N_{\alpha ,+1/2}+N_{\alpha ,-1/2}$, and an exact theorem for the $\alpha =s,\eta$ vectors ${\vec{C}}_{\alpha }$ is established, simplifying the expressions for their components $C_{\alpha ,\gamma }$ associated with the spatial directions $\gamma =1,\cdots ,d$. The expectation values of the spin and charge current operator corresponding to $S_{\alpha }^z$ for all $4^{N_a}$ energy and momentum eigenstates are simply given by ${\sum }_{\sigma =\pm 1/2}{N}_{\alpha ,\sigma }{\vec{j}}_{\alpha ,\sigma }$. They can also be expressed as $p_{\alpha z}{\vec{C}}_{\alpha }$, where the dependence on $S_{\tau }$ of the $\alpha =s,\eta$ polarization $p_{\alpha }$, which determines the interval of spin and charge polarization, $p_{\alpha z}=2S_{\alpha }^z/N_{\alpha }\in [-p_{\alpha },p_{\alpha }]$, is found to be universal for all bipartite lattices. Our exact results contribute to a deeper understanding of the model's physics and provide valuable insight into the transport properties of condensed-matter materials—such as cuprate superconductors, graphene, and graphene-derived systems—as well as other quantum systems described by the model.

We investigate the nonequilibrium dynamics of a laser-pumped two-dimensional spinless Holstein model within a semiclassical framework, focusing on the melting and recovery of long-range charge-density-wave order. Accurately describing this process requires fully nonadiabatic electron–lattice dynamics, which is computationally demanding due to the need to resolve fast electronic motion over long timescales. By analyzing the structure of the lattice force during nonequilibrium evolution, we show that the force naturally separates into a smooth quasiadiabatic component and a residual bathlike contribution associated with fast electronic fluctuations. The quasiadiabatic component depends only on the instantaneous local lattice configuration, with its explicit time dependence encoding the evolving carrier population, and can be efficiently learned using machine-learning techniques, while a minimal Langevin description of the bath term captures the essential features of the recovery dynamics. Combining these elements enables efficient and scalable simulations of long-time nonequilibrium dynamics on large lattices, providing a practical route to access driven correlated systems beyond the reach of direct nonadiabatic approaches.

We present a comprehensive analysis of the two-dimensional uniform electron gas (2D-UEG, or more commonly 2DEG) at finite temperature, spanning a broad range of densities/coupling strengths $(0.01\le r_s\le 20)$ and temperatures/degeneracy parameters $(0.01\le \mathrm{\Theta }=k_{\text{B}}T/E_{\text{F}}\le 10)$. Within the self-consistent dielectric formalism, we construct 2D versions of the Singwi-Tosi-Land-Sjölander (STLS) and hypernetted-chain (HNC) approximation–based schemes. We benchmark the accuracy of the STLS and the HNC schemes against new state-of-the-art path-integral Monte Carlo data. We also report structural and thermodynamic properties across the full $(r_s,\mathrm{\Theta })$ phase diagram domain studied, identify regimes in which these schemes remain quantitatively reliable, and provide an accurate parametrization of the exchange-correlation free energy of the finite-temperature 2DEG.

The construction of consistent pseudopotentials for exchange-correlation approximations that depend on the kinetic energy density [meta-generalized gradient approximations (meta-GGAs)] is challenging because of their explicit orbital dependence. However, modern meta-GGAs use the kinetic energy density to distinguish between one- and many-electron regions of space, and therefore, the straightforward use of inconsistent, e.g., GGA-based pseudopotentials, can lead to substantial errors. We here discuss a scheme for constructing pseudopotentials that incorporate the atomic kinetic energy density in the spirit of a core correction. This considerably increases the accuracy of meta-GGA calculations that use pseudopotentials. Examples and tests are presented for the nonrelativistic and the relativistic Troullier-Martins pseudopotential scheme using real-space grid based calculations. We discuss future extensions of the scheme.

Ferrovalley materials are a promising option for achieving controllable valleytronic and topological states in van der Waals heterostructures (vdWHs). Through first-principles calculations, we demonstrate that a type-III ${\mathrm{MoTe}}_2/{\mathrm{Cr}}_2{\mathrm{S}}_3$ vdWH can host multiple magnetically tunable topological phases. The broken-gap band alignment promotes charge transfer between the ${\mathrm{Cr}}_2{\mathrm{S}}_3$ and ${\mathrm{MoTe}}_2$ layers. However, charge transfer occurs preferentially between valleys with the same spin polarization, resulting in spin-selective band inversion and gap opening. The resulting topological phase is governed by the magnetization direction. With out-of-plane magnetization, a gap primarily opens at a single $K$ or $K^{\prime }$ valley, producing a valley-polarized quantum anomalous Hall state with one chiral edge state. In contrast, in-plane magnetization opens gaps at both $K$ and $K^{\prime }$ valleys, producing counterpropagating edge states that are characteristic of a time-reversal-symmetry-broken valley-polarized quantum spin Hall state. Furthermore, altering the stacking configuration and reversing the magnetization direction enables control over the sign of the Berry curvature and the activation or suppression of topological band inversion at the two valleys. These findings establish type-III ferrovalley vdWHs as a versatile platform for engineering spin-selective anomalous Hall responses and tunable topological valley transport.

Strain engineering serves as an effective approach for tuning diverse properties in quantum materials and electronic devices. One may establish a dual Hall effect based on the systematic response to the uniaxial strain induced symmetry reduction in multifunctional materials. Here, we predict a stable two-dimensional altermagnet monolayer ${\mathrm{Ta}}_2{\mathrm{Te}}_2\mathrm{O}$, which is a direct gap semiconductor. More interestingly, the magnetic anisotropy energy of monolayer ${\mathrm{Ta}}_2{\mathrm{Te}}_2\mathrm{O}$ shows the rare biaxial anisotropy in the xy plane, while exhibiting conventional uniaxial anisotropy in the xz plane. The four-leaf-clover-shaped magnetic anisotropy in the xy plane originates from the fourth-order single-ion interactions. Importantly, uniaxial strain can not only induce ${\mathrm{Ta}}_2{\mathrm{Te}}_2\mathrm{O}$ to transform from a semiconductor to a semimetal, but also effectively tune the direction and magnitude of valley polarization. Therefore, when the magnetization direction changes in the xy plane, the variation laws of valley splitting in the valence and conduction bands are exactly opposite to each other. In addition, uniaxial strain can break inversion symmetry, thereby inducing the anomalous Hall effect and nonlinear Hall effect. Our work demonstrates that two-dimensional altermagnets serve as an ideal platform for multifunctional devices, bridging linear and nonlinear magnetoelectric effects via strain engineering.

We report a direct observation of the electronic structure of monolayer SnTe on graphene by angle-resolved photoemission spectroscopy. By combining low-energy electron diffraction, momentum microscopy, core-level spectroscopy, and first-principles calculations, we show that the observed monolayer-limit electronic structure is consistent with a puckered even-layer biatomic-layer building block rather than a nonpuckered square-flat structure. The observed band dispersion and its polarization dependence are reproduced by a puckered structure with a substrate-renormalized buckling amplitude. We further show that graphene actively interacts with ultrathin SnTe by selecting its in-plane orientational texture, renormalizing the buckling amplitude, and modifying the local interfacial electrostatic environment in the monolayer limit. In comparison, multilayer SnTe exhibits a more ringlike momentum-space distribution, interlayer-split valence bands, and a stronger $p$-type character, revealing the onset of thickness evolution from an interface-stabilized puckered ultrathin limit toward a more bulklike state.

We investigate the magnetic orders and excitations in a half-filled Hubbard model that continuously interpolates between the Lieb and kagome lattices. Using the self-consistent Hartree-Fock approximation combined with the Bethe-Salpeter equation in the random phase approximation, we map the $U-t^{\prime }$ phase diagram of the Lieb-kagome lattices and compute real-frequency transverse spin susceptibilities, i.e., the magnon spectra. Dynamical mean-field theory and exact diagonalization are used as complementary checks of static magnetic phases. In particular, besides gapless Goldstone magnons, the symmetry-broken ferrimagnetic and antiferromagnetic phases also exhibit gapped Higgs magnon bands, which originate from amplitude fluctuations in the order parameter characterizing spontaneous symmetry breaking.