We derive a contrast expansion formalism for the effective conductivity of heterogeneous materials (media) with local properties described by arbitrary continuous random fields, significantly generalizing the widely used two-phase (binary-field) models. The theory produces a rapidly convergent Neumann series that, upon Gaussian closure via a Hermite expansion, yields closed-form first-, second-, and third-order approximations, which achieve percent-level accuracy at first order for isotropic media. For anisotropic media, second-order approximations achieve sub-$2\%$ accuracy across a wide range of local property contrasts and correlations. Our formalism provides mathematically rigorous structure-property closures, with significant implications for the discovery and design of graded and architected materials with tailored transport properties.

We study the nonequilibrium dynamics of a binary disordered alloy when it is subjected to an interaction quench. Our study uses a nonequilibrium embedding scheme $(\mathrm{DMFT}+\mathrm{CPA})$ that combines the capacity of DMFT (dynamical mean field theory) to treat strongly correlated systems and the capacity of CPA (coherent potential approximation) to treat disordered systems, to effectively address the interplay of disorder and interaction for the nonequilibrium system. Our solution is applied on the equilibrium binary disordered and interacting alloy for the calculation of the density of states. This equilibrium density of states shows the modifications of the disorder-driven gap by the interaction and that of the interaction-driven Mott gap by the disorder. Next, we assess the relaxation of the system that is initially in equilibrium at a given temperature, and then abruptly has its interaction strength changed from zero to a finite value at which it is kept constant. The system undergoes a short time transient and then settles into a longtime state in a process that depends in a nontrivial manner on the disorder and interaction strength. In addition, we calculate the effective temperature of the system after it has gone through its initial transient and settled into its longtime state. The longtime effective temperature is increased with increasing final interaction strength. However, for a given final interaction, the final temperature can be tuned by the disorder strength over a broad range, with stronger disorder leading to lower temperature. Altogether, the results illustrate the nontrivial interplay between disorder and interaction for a binary alloy away from equilibrium.

Numerical methods based on tensor networks have been extensively explored in the research of quantum many-body systems in recent years. It has been recognized that the ability of tensor networks to describe a quantum many-body state crucially depends on the spatial structure of the network. In the previous work [T. Hikihara et al., Phys. Rev. Res. 5, 013031 (2023)], we proposed an algorithm based on tree-tensor networks (TTNs) that automatically optimizes the structure of a TTN according to the spatial profile of entanglement in the state of interest. In this paper, we apply the algorithm to the random $\mathit{XY}$-exchange model under random magnetic fields and the Richardson model in order to analyze how the performance of the algorithm depends on the detailed updating schemes of the structural optimization. We then find that for the random $\mathit{XY}$ model, on the one hand, the algorithm achieves improved accuracy, and the stochastic algorithm, which selects the local network structure probabilistically, is notably effective. For the Richardson model, on the other hand, the resulting numerical accuracy subtly depends on the initial TTN and the updating schemes. In particular, the algorithm without the stochastic updating scheme certainly improves the accuracy, while the one with the stochastic updates results in poor accuracy due to the effect of randomizing the network structure at the early stage of the calculation. These results indicate that the algorithm successfully improves the accuracy of the numerical calculations for quantum many-body states, while it is essential to appropriately choose the updating scheme as well as the initial TTN structure, depending on the systems treated.

Two-dimensional (2D) anisotropic magnetic van der Waals (vdW) materials offer unique opportunities for tailoring magnetic properties via symmetry engineering. Here, we theoretically investigate how external electric fields modulate the magnetic interactions and spin dynamics in the anisotropic CrOCl monolayer. Our calculations demonstrate that electric fields break the inversion symmetry between Cr sublattices in the monolayer, lifting the degeneracy of intrasublattice exchange coupling. This symmetry breaking enhances the splitting of acoustic and optical magnon modes, particularly along high-symmetry directions. Additionally, the spin Seebeck coefficient, which governs spin current generation from temperature gradients, increases under electric fields. Our work uncovers the critical role of electric-field-tuned symmetry in tailoring magnetic interactions and spin dynamics in 2D anisotropic vdW magnets, and provides a promising strategy for engineering magnonic properties in 2D materials, paving the way for advanced spintronic applications.

In a Fermi system near or at half-filling, a specific superconducting pairing channel, if not explicitly included in the Hamiltonian, can be boosted by suppressing a competing pairing channel; this is exemplified by the enhancement of extended $s$-wave correlations upon suppressing $s$-wave Cooper pairing. This phenomenon, originally found by the use of generalized uncertainty relations is referred to as order by projection. The case of zero on-site Coulomb interaction in the thermodynamic limit, confirms this mechanism through the analytical solution. In this study, we go further and systematically investigate this mechanism for a strongly correlated fermionic Hubbard model, now with finite on-site interaction, on a square lattice with an extended set of hopping parameters. We explore the behaviors of different pairing channels when one of them is suppressed, utilizing density matrix renormalization group calculations. Our findings provide numerical evidence supporting the existence of order by projection in the strongly correlated system we studied. We also investigate the effect of the strength of Hubbard $U$, next-nearest-neighbor $t^{\prime }$, hole doping, as well as finite-size scaling approaching the thermodynamic limit.

We investigate the permittivity of helium (He) in perovskite-group ${\mathrm{KNbO}}_3$ and its high-pressure polymorphs using Raman scattering. Samples were loaded into either an argon (Ar) or He pressure medium to fingerprint the incorporation of He. Specifically, our high-pressure in situ Raman spectroscopy experiments reveal that He has permeated into the high-pressure tetragonal and cubic perovskite phases, while the ambient orthorhombic phase can hold little He. In contrast, Ar is impermeable into ${\mathrm{KNbO}}_3$ under pressure and the results are consistent with previous studies. We further validate the incorporation of He into the lattice sites of ${\mathrm{KNbO}}_3$ by using both the disorder effect and Fano resonance analyses. The structural selectivity behavior of He suggests that minerals could potentially induce He concentration heterogeneity within Earth's interior.

The two-dimensional (2D) XY model plays a crucial role in statistical and condensed-matter physics. With the introduction of long-range interactions, the system exhibits a richer set of physical phenomena and a crossover between nonclassical and short-range universality classes. In this work, we investigate the 2D XY model with algebraically decaying interactions $\sim 1/r^{2+\sigma }$ and provide a comprehensive numerical analysis of its thermodynamic properties. We demonstrate that for $\sigma \le 2$, the system undergoes a second-order phase transition into a ferromagnetic phase characterized by the emergence of long-range order. In the low-temperature phase, due to the presence of the Goldstone mode, the correlation function saturates to a nonzero constant in the form of a power law for $\sigma <2$, with decaying exponent $2-\sigma$, and in the form of the inverse logarithm of distance for $\sigma =2$. Moreover, the critical points and exponents are also determined for various $\sigma$. We provide compelling evidence that the crossover between nonclassical and short-range regimes occurs at $\sigma =2$. This work presents a detailed account of the simulation methodology, extensive numerical data, and new insights into the physics of long-range interacting systems.

${\mathrm{Sr}}_2{\mathrm{IrO}}_4$, a prototypical $J_{\mathrm{eff}}=1/2$ square lattice system, is widely studied for novel physics. While transition metal substitution effects are well explored, rare-earth doping at the ${\mathrm{Ir}}^{4+}$ site is less explored. Here we present a detailed magnetization and neutron diffraction study on ${\mathrm{Sr}}_2{\mathrm{Ir}}_{1-x}{\mathrm{Tb}}_x{\mathrm{O}}_4$ $(x=0.11)$. The system tends to adopt an in-plane antiferromagnetic configuration with a “$++++$” stacking sequence. Strong spin fluctuations persist down to the lowest measured temperature, consistent with the concave shape order parameter. A pronounced magnetic diffuse scattering rod develops along the $L$ direction at low temperature, indicating the formation of short-range magnetic correlations with a characteristic length of $\sim 24\left(2\right)\AA$. This work provides a new pathway to exotic quantum phases in the strongly spin-orbit-coupled iridates.

Two-dimensional intrinsic magnets with multiple magnetic atomic layers often allow the magnetic phase and the magnetic anisotropy transitions, providing a versatile platform for exploring monolayer spin valve and magneto-optical effects. Based on the first-principles calculations and Monte Carlo simulations, both spin valve and magneto-optical effects emerge from the strained ${\mathrm{Cr}}_2{\mathrm{Te}}_3$ monolayer. The ${\mathrm{Cr}}_2{\mathrm{Te}}_3$ monolayer is a ferromagnetic metal with an in-plane easy magnetization axis and a Curie temperature of 495 K. Under the tensile strain up to 4.2%, it transitions to an antiferromagnetic semiconductor. The direction of the easy magnetization axis changes to an out-of-plane direction during strains from 1% to 4%, and also induces a variance of the Kerr rotation angle through the magneto-optical Kerr effect. We provide a potential candidate material for the design of a future room-temperature monolayer spin valve and optospintronic devices.

Unconventional charge density waves (CDWs) have been observed in the kagome superconductor ${A\mathrm{V}}_3{\mathrm{Sb}}_5$ $(A=\mathrm{K}, \mathrm{Rb}, \text{or} \mathrm{Cs})$, which exhibit extraordinary symmetry breaking and intertwine with superconductivity (SC). Here, via ${}^{51}\mathrm{V}$ nuclear magnetic resonance (NMR), we reveal that a new CDW modulation is developed locally around dopants in ${\mathrm{CsV}}_{3-x}{\mathrm{Ti}}_x{\mathrm{Sb}}_5$, which leads to the suppression of the long-range triple-Q CDW. With slight Ti substitution $(x<0.09)$, a rapid increase in Knight shift and a progressive decrease in $1/T_{1}T$ are observed, which is beyond the simple picture of the suppression of the triple-Q CDW. Above $x=0.12$, while the CDW transition is absent in specific heat measurements, a gap behavior is still observed in the local spin susceptibilities. By quantitatively analyzing the doping-dependent NMR line shape and $1/T_{1}T$, we propose that a competitive CDW with unidirectional modulation is locally formed around Ti dopants, which is key to explaining the unusual evolution of the CDW and SC in ${\mathrm{CsV}}_{3-x}{\mathrm{Ti}}_x{\mathrm{Sb}}_5$. In this picture, the persisting gap behavior above $x=0.12$ comes from the short-range CDW matrix. In addition, our present NMR results highlight the role of the next-nearest-neighboring V-V interaction in CDW driving. All these findings substantiate vanadium-based kagome superconductors as strongly coupled electron-lattice systems, which is a basis for understanding unconventional CDWs and their role in SCs.

We study a double layer superconductor in the presence of a parallel magnetic field $B$ by obtaining self-consistent solutions of the Bogoliubov–de Gennes equations, and also using the Pokrovsky-Talapov model for the free energy expressed in terms of the relative phase, namely the difference in the phases of the superconducting order parameters in the two layers. We find that with increasing $B$ a continuous transition occurs from the BCS state, where the relative phase is constant, into a state which contains stripes of the BCS state separated by localized vortices in the relative phase. This state is predicted to manifest through oscillations in the amplitude of the superconducting gap and an alternating pattern of supercurrents. With increasing $B$, the BCS stripe state continuously evolves into the Fulde-Ferrell-Larkin-Ovchinnikov state with linearly varying relative phase and a constant gap amplitude. These predictions apply to superconductivity in bilayer transition-metal-dichalcogenide systems with Ising spin-orbit coupling, and ought to be testable in a recently studied experimental system.

The pressure-induced spin crossover in divalent cobalt is studied. It is shown that the change in spin as a function of pressure and its effects on $K_{\beta }$ x-ray emission depend on the $3d$ spin-orbit interaction and local exchange fields, leading to a broadening of the spin-crossover transition as a function of octahedral crystal field or pressure. A detailed comparison is made with experimental data on ${\mathrm{Na}}_3{\mathrm{Co}}_2{\mathrm{SbO}}_6$ as a function of the octahedral field tuned by pressure. Additionally, the spectral weight of the $K_{{\beta }^{\prime }}$ feature is studied for transition metals, and the Tsutsumi rules [K. Tsutsumi, J. Phys. Soc. Jpn. 14, 1696 (1959); K. Tsutsumi and H. Nakamori, J. Phys. Soc. Jpn. 25, 1418 (1968); K. Tsutsumi et al., Phys. Rev. B 13, 929 (1976)] are reexamined.

We report a systematic investigation of the physical properties and Fermi-surface topology of layered single-crystal ${\mathrm{SrCu}}_4{\mathrm{As}}_2$ using electrical transport, magnetotransport, and quantum-oscillation experiments plus band-structure calculations. The temperature-dependent electrical resistivity reveals a hysteretic phase transition at $T_P=59$ K, most likely associated with a structural change. Hall resistivity data suggest a marked change in the average hole density resulting from the latter phase transition near $T_P$. A large, linear, and nonsaturating magnetoresistance is observed at low temperatures in ${\mathrm{SrCu}}_4{\mathrm{As}}_2$, likely attributable to the multipocket Fermi surface. Quantum-oscillation data measured in magnetic fields of up to 60 T show several oscillation frequencies exhibiting low effective masses, indicating the presence of Dirac-like band dispersion in ${\mathrm{SrCu}}_4{\mathrm{As}}_2$, as suggested by the band structure calculations.

We investigate equilibrium (background), linear, and nonlinear spin currents in two-dimensional Rashba spin-orbit coupled altermagnet systems, using a modified spin current operator that includes anomalous velocity arising from nonzero Berry curvature. The background spin current, stemming from spin-orbit coupling and modulated by the altermagnet term ($t_j$), exhibits in-plane polarization, increases linearly with Fermi energy (${\epsilon }_F$), and is enhanced by both the altermagnet ($t_j$) and the Rashba parameter ($\lambda$). Linear spin current is always transverse with out-of-plane polarization and can be viewed as a spin Hall current, primarily driven by band velocity, with $t_j$ enabling a band-induced contribution [previously absent in simple Rashba systems ($t_j=0$)]. This highlights the altermagnet system as a promising source of spin Hall current generation. For linear spin Hall current, its band contribution's magnitude increases linearly with ${\epsilon }_F$, while the magnitude of the anomalous component saturates at higher ${\epsilon }_F$. Further, the magnitude of the spin Hall current is enhanced by $t_j$ but reduced by $\lambda$. Nonlinear spin currents feature both longitudinal and transverse components with in-plane polarization. Both the nonlinear longitudinal spin current from band velocity and the nonlinear transverse spin current from anomalous velocity initially decrease with ${\epsilon }_F$ before saturating at higher ${\epsilon }_F$. Importantly, $t_j$ reduces these currents while $\lambda$ enhances them. Meanwhile, the nonlinear transverse current from band velocity increases and then saturates with ${\epsilon }_F$, enhanced by $\lambda$ and showing nonmonotonic variation with $t_j$. These findings highlight the tunability of spin current behavior through Rashba and altermagnet parameters, offering insights for spintronic applications.

The tedious parametrization process remains a key bottleneck hindering broader adoption of the empirical tight-binding method. Here, we discuss the challenges and requirements of finding parameters for Slater-Koster-based empirical tight-binding schemes, and explain the shortcomings of the parametrization procedures commonly used in the literature. We then propose our way to address these challenges, through the presentation of an open-sourced parametrization toolbox that breaks up the task into several, incremental stages. The prototype of our toolbox is tailored especially to deal with a recently proposed, highly transferable scheme, but can be easily adapted to any Slater-Koster-based scheme. A case study of fitting GaN parameters is considered. Remarkably, the obtained GaN parameter set shows high transferability when applied to various contexts: from simple zincblende or wurtzite bulk cases, to polytypic heterostructures and even highly mismatched alloys in their dilute limits. This confirms the effectiveness and robustness of our parametrization approach.

Trions, charged quasiparticles formed by binding an exciton to an excess charge carrier, dominate the optical response of doped transition metal dichalcogenides (TMDs), and the study of the transport properties of trions in TMDs may have applications in developing high-speed excitonic and optoelectronic devices. However, an important building block for low-dissipation optoelectronic devices that provides dissipationless transport channels for trions has remained elusive. Here, we propose the concept of a ${\mathbb{Z}}_2$ topological trion insulator that features helical dissipationless edge states for trions. This is realized for intralayer trions, which inherit the valley-orbit coupling of intralayer excitons in TMDs subject to a moiré periodic potential. We find that under certain circumstances, the moiré trion band becomes topological, characterized by the ${\mathbb{Z}}_2$ topological number. We further provide two specific material realizations of this ${\mathbb{Z}}_2$ topological insulator: a doped monolayer TMD placed on top of a twisted hBN substrate, and a generic twisted TMD heterobilayer. We also examine the effect of charge screening and find that the ${\mathbb{Z}}_2$ topological trion insulator remains robust. Our work paves the way toward realizing dissipationless excitonic and trionic devices.