We present temperature-dependent Raman spectra of semimetallic $1T\text{−}{\mathrm{Ti}}_{1.03}{\mathrm{S}}_2$ single crystals measured from 6 to 300 K using a 532 nm excitation laser and identify a change in the phonon line shape near the Raman crossover temperature $T_c^R$ = 180 K. At 6 K, the Raman spectrum exhibits the first-order $E_g$ and $A_{1g}$ phonon modes, and a shoulder mode (Sh) at a frequency higher than that of the $A_{1g}$ phonon mode. All three phonon modes exhibit asymmetric line shapes that are described by the Breit-Wigner-Fano (BWF) function. The BWF asymmetry parameters $1/q$ of the $A_{1g}$ and Sh modes change above $T_c^R$ = 180 K, suggesting mutual interference between these two modes. The peak intensity $I_0$ of the Sh mode decreases more slowly than those of the $E_g$ and $A_{1g}$ phonon modes below 180 K, whereas its spectral linewidth ${\mathrm{\Gamma }}_0$ increases more rapidly above 180 K. These observations support the assignment of the Sh mode to a two-phonon double-resonance Raman process involving the $A_{1g}$ phonon and an acoustic phonon. A piecewise power-law analysis of the temperature-dependent electrical resistivity gives a different crossover temperature, $T_c$ = 132.6 K, suggesting a gradual crossover of the electronic structure of $1T\text{−}{\mathrm{Ti}}_{1.03}{\mathrm{S}}_2$ over a broad temperature range from 100 to 200 K.

We found a spin-orbit coupling to cause a simultaneous correlation among 3 degrees of freedom, the electronic spin, orbital, and Bloch dynamics in an investigation into the electronic structure of Janus double-transition-metal MXenes, ${\mathrm{Mo}}_2{\mathrm{HfC}}_2\mathrm{OS}$ and ${\mathrm{W}}_2{\mathrm{HfC}}_2\mathrm{OS}$. In this paper, it is also revealed that the spin-orbit coupling causes a staggered spin configuration with a trigonal pattern around the $\mathrm{\Gamma }$ point near the insulating gap. We developed a reduced Hamiltonian describing the electronic states and show that the spin-orbit coupling cannot be equated with conventional forms for a single electron in solids, LS, Rashba, and Dresselhaus couplings, even in the approximation under the low-energy and small wave-number condition. Because of the intrinsic shape of the conduction band, a trigonally alternating spin-momentum locking emerges with the spin axis perpendicular to the layer plane. The theoretical analysis shows that these Janus materials can provide a platform for exploring the spin-related phenomena due to the trigonal spin-momentum locking other than Rashba and Dresselhaus types.

The hypergraph product (HGP) construction of quantum error-correcting codes (QECCs) offers a general and explicit method for building a QECC from two classical codes, thereby paving the way for the discovery of good quantum low-density parity-check codes. In this paper, we propose a general and explicit construction recipe for QECCs from a total of $D$ classical codes for arbitrary $D$. Following this recipe guarantees a valid QECC within the stabilizer formalism and enables the systematic exploration of a broad class of constructions. As examples, we demonstrate that our construction recovers the HGP construction when $D=2$ and leads to four distinct types of constructions for $D=3$, including a previously studied case as one of them. When the input classical codes are repetition codes, our $D=3$ constructions unify various three-dimensional lattice models into a single framework, encompassing the three-dimensional toric code model, a fracton model, and two other intriguing models not previously investigated. Among these, two types of constructions exhibit a trade-off between code distance and code dimension for a fixed number of qubits by adjusting the lengths of the different classical codes, and the optimal choice can simultaneously achieve relatively large values for both code distance and code dimension. Our general construction protocol provides another perspective for enriching the structure of QECCs and enables the exploration of richer possibilities for good codes.

The $GW$ method delivers substantially improved accuracy in electronic band structure calculations over conventional Kohn–Sham density functional theory (KS-DFT) by explicitly incorporating the electron self-energy effect beyond mean-field approximations. In this work, we present an efficient NAO-PP-based $G^0{W}^0$ computational framework by interfacing the first-principles software package abacus with librpa, a library for performing low-scaling random-phase approximation and $GW$ calculations based on NAOs. Our approach employs the localized resolution of identity (LRI) technique with a compression scheme, significantly improving both computational efficiency and numerical stability. In addition, an analytic treatment of the small-$\mathbf{q}$ limit of the microscopic dielectric function reduces the need for dense $\mathbf{q}$-point sampling. Furthermore, we quantify how the choice of explicitly treated valence electrons affects the frequency-dependent macroscopic dielectric response and the resulting $G^0{W}^0$ quasiparticle energies. Systematic benchmarks validate the effectiveness of our compression scheme and real-space tensor filtering strategies, demonstrating both high accuracy and significant computational efficiency gains. Comparisons with established $G^0{W}^0$ implementations show excellent agreement in band structures and band gaps, confirming $\mathrm{ABACUS}+\mathrm{LibRPA}$ as a reliable and efficient platform for large-scale $G^0{W}^0$ simulations.

Collective excitations of many-body electron systems can carry internal structure, supporting novel quantum geometric and topological properties. Among these are a quantum geometric dipole (QGD), which for excitons have direct significance as an internal polarization. For interlayer excitons of a bilayer system, this represents an in-plane dipole moment, which can be used to drive them with in-plane electric fields. In this work, we consider counterflow electric currents associated with driven excitons in such a bilayer system as a probe of their QGD structure. As a simple but nontrivial example, we analyze a structure with a one-dimensional periodic potential in a strong perpendicular magnetic field. The resulting magnetoexciton bands host QGD structure that distinguishes it from the exciton QGD of a uniform system. To model exciton transport we adopt a Boltzmann approach that includes interband tunneling, allowing us to consider nonequilibrium momentum distributions that result from strong layer-antisymmetric driving fields. We show how linear response to a layer-symmetric component of the driving fields provide information about the QGD, and that the broad QGD structure of the exciton bands can be probed by the varying the layer-antisymmetric field. Our results demonstrate that counterflow conductivity serves as a tunable probe of the internal quantum geometric structure carried by the interlayer excitons, connecting transport to the quantum geometry of many-body excitations.

We study the entanglement properties of the one-dimensional dimerized Fermi-Hubbard model. Using a matrix product state approach, we compute the ground state and identify two insulating phases at 1/2- and 3/4-filling, along with a metallic phase. The underlying physical mechanisms of these phases are conclusively characterized by their entanglement spectra. Our findings demonstrate that the two insulating phases are physically distinct: the phase at 1/2-filling possesses a charge gap originating from the robust band gap enhanced by repulsive interactions, whereas the phase at 3/4-filling exhibits a Mott gap resulting from electron interactions. This fundamental distinction is faithfully reflected in the finite-entanglement scaling properties of the half-chain entanglement entropy and the universal distribution of the entanglement spectrum.

Local gauge structures play a central role in a wide range of condensed matter systems and synthetic quantum platforms, where they emerge as effective descriptions of strongly correlated phases and engineered dynamics. We introduce a gauge-invariant graph neural network (GNN) architecture for Abelian lattice gauge models, in which symmetry is enforced explicitly through local gauge-invariant inputs, such as Wilson loops, and preserved throughout message passing, eliminating redundant gauge degrees of freedom while retaining expressive power. We benchmark the approach on both ${\mathbb{Z}}_2$ and $\mathrm{U}\left(1\right)$ lattice gauge models, achieving accurate predictions of global observables and spatially resolved quantities despite the nonlocal correlations induced by gauge–matter coupling. We further demonstrate that the learned model serves as an efficient surrogate for semiclassical dynamics in $\mathrm{U}\left(1\right)$ quantum link models, enabling stable and scalable time evolution without repeated fermionic diagonalization, while faithfully reproducing both local dynamics and statistical correlations. These results establish gauge-invariant message passing as a compact and physically grounded framework for learning and simulating Abelian lattice gauge systems.

The realization of half-metallicity in two-dimensional materials is of considerable interest for the development of nanoscale spintronic devices. In this work, we systematically investigate the electronic structure and spin-dependent quantum transport properties of substitutionally Mo-doped GaSe monolayers using first-principles calculations combined with the nonequilibrium Green's function formalism. Our results show that Mo substitution induces half-metallic behavior in intrinsically nonmagnetic GaSe. Driven by strong $p\text{–}d$ hybridization and substantial on-site exchange splitting, the spin-down channel exhibits a wide energy gap of 1.65 eV, resulting in highly spin-selective transport. Within the collinear spin-conserving transport framework employed here, the calculated spin-filtering efficiency reaches 100% under all finite bias voltages within the range of $\pm 0.5\mathrm{V}$. The spin-up channel also exhibits pronounced negative differential resistance and a magnetoresistance ratio exceeding ${10}^{11}$. Real-space analysis further reveals that the spin-polarized transport is mediated by a rhombic reticular nanochannel whose bias-driven evolution from a continuous resonant network to discretized islands affects the current response. These results suggest that Mo-doped GaSe is a promising candidate for spin-filtering and related spintronic applications.

At terahertz drive frequencies, magnetization dynamics enter an inertial regime beyond the scope of standard Landau-Lifshitz-Gilbert (LLG) theory. We reveal a nutational damping torque comprising a bulk term and an interfacial contribution that describes spin emission into adjacent metals. The interfacial term generates nutational spin pumping: a dc spin current that scales quadratically with the drive frequency. Using a scattering approach, we relate this effect to microscopic material parameters and predict pronounced enhancements in ultrathin films and low Fermi-energy conductors. Nutational spin pumping can be detected directly via the inverse spin Hall effect or indirectly via thickness-dependent renormalization of nutational damping.

Topological phase transitions are typically characterized by abrupt changes in a quantized invariant. Here we report a contrasting paradigm in spontaneous parity-time symmetry-breaking transitions induced by non-Hermiticity. The topological invariant remains conserved, but its nature transitions between the Chern number, characteristic of chiral transport in complex bands, and the Euler number, which characterizes the number of nodal points in pairs of real bands. This conserved morphing of topological properties applies to all pairs of bands whose spectral gaps to other bands remain open during the transition. It features qualitative changes in the non-Abelian geometric phases, which quantize in different forms across the transition. Our findings establish a generic topological duality principle governing transitions across symmetry classes and reveal unique connections among topology, symmetry, and non-Abelian gauge structure in nonunitary processes.

The response of the Fermi energy to external perturbations governs key physical observables at metallic interfaces. Although this response admits a local formulation in terms of the Fukui function, its evaluation has traditionally been limited by inherent approximations, fundamentally rooted in the difficulty of adding a finite charge in a periodic system. We present an exact resolution to this problem that, within an electronic-structure framework capturing metallic behavior, exploits the screening properties of electronic conductors to compute Fukui functions via a finite electric field. The resulting linear-response theory yields strictly quadratic error scaling of Fermi-level shifts across representative platinum surfaces, achieving sub-meV accuracy up to fields of 0.1 V/Å. The approach is further validated by reproducing work-function changes under molecular perturbations, and by providing mean-field estimates of electrode potentials that yield capacitance-voltage curves consistent with experiment. Our findings establish a rigorous foundation for a local theory relating electrostatic screening and Fermi-energy variations at metallic interfaces.

Polar antivortices are fundamental topological defects in ferroelectric polarization fields, yet their deterministic formation and manipulation remain largely unexplored. Here, using phase-field simulations, we demonstrate chirality-mediated programming of polar textures in ${\mathrm{PbTiO}}_3/{\mathrm{SrTiO}}_3$ (PTO/STO) ferroelectric-dielectric nanostripes. Ferroelectric vortices are stabilized in PTO nanostripes, while diverse polar textures, including two topologically nontrivial antivortex states and two topologically trivial configurations, emerge in STO through epitaxial strain and interfacial polarization coupling. Although the two antivortex states possess identical winding topology, their distinct polarization geometries enable unambiguous identification through complementary topological and angular analyses. We reveal that STO polar textures are deterministically governed by the chirality arrangement of neighboring PTO vortices, establishing a direct link between parent vortex chirality and emergent polar configurations. Temperature, electrostatic screening, and epitaxial strain are systematically explored to construct phase diagrams of texture stability and switching. A scanning Gaussian electric field enables active manipulation of PTO vortex chirality and programmable transformation among STO polar states. These findings establish a strategy for chirality-mediated programming of ferroelectric topological textures and provide opportunities for designing electrically reconfigurable topological polar states in oxide heterostructures.

Several candidate reference phases have been proposed to discuss phase transitions and ferroelectricity in hafnia in recent years. Although these proposals comply with crystallographic requirements, a physically compelling rationale connecting parent and daughter phases is often lacking. This problem is aggravated by the absence of clearly dominant polarization switching pathways, making it difficult to formulate a robust physical criterion for identifying the relevant high-symmetry states. Here, we use first-principles calculations to show that pressure reveals clear parent-daughter relationships among many polymorphs of hafnia and thereby provides a physically motivated hierarchy of structures, including the monoclinic ground state and the technologically relevant ferroelectric phase, and their respective parent structures. Our simulations also reveal several additional phases, including higher-energy structures that act as common ancestors of the widely discussed cubic and orthorhombic reference phases.

Negative linear compressibility (NLC) describes a unique property of certain materials that expand in one direction when exposed to external pressure. Solid electrolytes with this counterintuitive effect offer a promising opportunity to enhance the lithium-ion conductivity, as the directional expansion can facilitate the creation of improved ion transport pathways. Here, we reported a high-pressure-induced phase transition in ${\mathrm{Li}}_4{\mathrm{SiW}}_{12}{\mathrm{O}}_{40}$ from the Keggin to the bronze structure. This high-pressure phase remained stable under ambient conditions after decompression, and exhibited the unconventional mechanical behavior of NLC with a compression coefficient $K_{\mathrm{c}}=-9{\mathrm{TPa}}^{-1}$. This transition enhanced lithium-ion conductivity by more than an order of magnitude, from $0.018$ to $0.22\mathrm{mS}{\mathrm{cm}}^{-1}$. The NLC effect synergistically expanded the migration channels and shortened the ${\mathrm{Li}}^{+}\text{−}{\mathrm{Li}}^{+}$ distance from 5.92 to 3.34 Å, collectively lowering the migration barrier. Concurrently, the NLC-induced formation of highly distorted ${\mathrm{Li}}^{+}$ sites within ${\mathrm{SiO}}_5$ polyhedra weakened the binding energy between ${\mathrm{Li}}^{+}$ and the framework. This promoted the formation of new bonds, which shortened interatomic distances and concentrated electron density. The resultant electronic redistribution contracted the transition-state volume, thereby generating a negative activation volume, which indicated higher carrier mobility. These findings provide new approaches for enhancing the conductivity of lithium-ion electrolytes.

Spin-canting in antiferromagnetic transition metal oxides originates from the competition of the Dzyaloshinskii-Moriya interaction and single-ion anisotropy with a relatively stronger superexchange interaction. Here we find canted antiferromagnetism in a disordered orthorhombic double perovskite, namely ${\mathrm{Pr}}_2{\mathrm{CrMnO}}_6$. The magnetic structure of ${\mathrm{Pr}}_2{\mathrm{CrMnO}}_6$ is investigated by performing structure, spectroscopy, dc magnetization, and temperature dependent neutron diffraction measurements. The dc magnetization measurements in combination with temperature dependent neutron diffraction measurements reveal a magnetic transition below 95 K, likely resulting from Cr-Mn ordering. Neutron diffraction confirms canted antiferromagnetic order below 95 K with a ground state canting angle of ${38}^{\circ }$ and significant structure-magnetism correlation around the magnetic transition temperature. The canted nature of Cr/Mn moments is attributed to Dzyaloshinskii-Moriya interaction and tilting of the Mn/Cr-${\mathrm{O}}_6$ octahedra, which determine the local easy axes of magnetization. Magnetocaloric studies reveal a second-order magnetic phase transition of the Cr-Mn sublattice at 95 K. The experimentally observed electronic and magnetic ground states are further supported by density functional theory calculations.

We derive analytically, and validate numerically, the dispersion renormalization and attenuation of acoustic waves propagating through quenched disordered media in the long-wavelength limit. We consider weak spatial fluctuations in elastic moduli and/or mass density and compute the disorder-induced self-energies within the leading (Born) approximation. For sufficiently weak disorder, the results depend only on the variances of the fluctuations and are therefore insensitive to the detailed form of the underlying random distribution. For spatially uncorrelated elastic disorder we obtain Rayleigh-type attenuation, $\mathrm{\Gamma }\left(q\right)\propto q^{d+1}$, together with a reduction of the sound speed. In contrast, density disorder produces Rayleigh-type attenuation but does not renormalize the acoustic dispersion to leading order. Molecular dynamics simulations and normal-mode analyses of disordered one- and two-dimensional lattices quantitatively confirm the theoretical predictions.

Ising spin-orbit coupling (ISOC) can strongly protect superconductivity against exchange-field-induced depairing, typically leading to critical fields far exceeding the Pauli limit and continuous (second-order) phase transitions. Here, using a standard free-energy approach, we demonstrate that first-order transitions can emerge in superconductors with weak ISOC under large exchange fields. In this regime, theoretical approaches based on the gap equation fail to determine the thermodynamic critical field and instead yield only the supercooling field. We further identify two pronounced in-gap coherence peaks in the quasiparticle spectra, which represent the weak-ISOC manifestation of the previously reported mirage-gap states. These thermodynamic and spectroscopic signatures remain robust against modest impurity scattering and provide experimentally accessible criteria for identifying weak Ising superconductivity, which serves as an intermediate regime between conventional Pauli-limited and strong Ising superconductors.

We theoretically investigate the magnetic and crystalline anisotropies of the superconducting diode effect (SDE) in proximitized planar Josephson junctions (JJs) with coexisting Rashba and Dresselhaus spin–orbit couplings (SOCs) under an in-plane magnetic field. A symmetry analysis identifies geometric constraints on magnetic-field and crystallographic orientations for which the SDE is suppressed independently of the field strength, providing experimentally testable signatures of the interplay between SOC and Zeeman interaction. We develop a phenomenological model showing that the diode efficiency depends on the relative alignment between the spin–orbit and magnetic fields, and corroborate this behavior in the narrow-junction, low-field regime using an analytical approach that links the anisotropy of the diode response to SOC-induced Fermi contour distortions and anisotropic Cooper pair momentum. These findings are supported by tight-binding simulations of the Bogoliubov–de Gennes equation, which reproduce recent experimental trends. The simulations reveal that electrostatic gating can induce polarity reversals of the SDE in the low-field regime even with only Rashba SOC, consistent with recent experiments, and predict additional reversals for specific field orientations, junction geometries, and SOC ratios. Our results elucidate the origin of anisotropic nonreciprocal superconducting transport and provide guidance for experimentally probing the mechanisms underlying the SDE in semiconductor-based planar JJs.