Compared to the ferromagnetic materials that realize the anomalous valley Hall effect by breaking time-reversal symmetry and spin-orbit coupling, the antiferromagnetic materials with joint spatial inversion and time-reversal $\left(PT\right)$ symmetry are rarely reported to achieve the anomalous valley Hall effect. Here, we predict that the antiferromagnetic monolayer MnBr possesses spontaneous valley polarization. The valley splitting of the valence band maximum is 21.55 meV at $K$ and $K^{\prime }$ points, which originates from $\mathrm{Mn}\text{−}{d}_{x^2-y^2}$ orbital by analyzing the effective Hamiltonian. Importantly, monolayer MnBr has zero Berry curvature in the entire momentum space but nonzero spin-layer locked Berry curvature, which offers the condition for the anomalous valley Hall effect. In addition, the magnitude of valley splitting can be signally tuned by the strain, magnetization rotation, electric field, and built-in electric field. The electric field and built-in electric field induce spin splitting due to breaking the $P$ symmetry. Therefore, the spin-layer locked anomalous valley Hall effect can be observed in MnBr. More remarkably, the ferroelectric substrate ${\mathrm{Sc}}_2{\mathrm{CO}}_2$ can tune monolayer MnBr to realize the transition from metal to valley polarization semiconductor. Our findings not only extend the implementation of the anomalous valley Hall effect, but also provide a platform for designing low-power and nonvolatile valleytronics devices.

We propose an analytical thermodynamic model for describing defect phase transformations, which we term the statistical phase evaluation approach (SPEA). The SPEA model assumes a Boltzmann distribution of finite-size phase fractions and calculates their statistical average. To benchmark the performance of the model, we apply it to construct binary surface phase diagrams of metal alloys. Two alloy systems are considered: a Mg surface with Ca substitutions and a Ni surface with Nb substitutions. To construct a firm basis against which the performance of the analytical model can be leveled, we first perform Monte Carlo (MC) simulations coupled with cluster expansion of a density functional theory dataset. We then demonstrate that the SPEA model reproduces the MC results accurately. Specifically, it correctly predicts the surface order-disorder transitions as well as the coexistence of the 1/3 ordered phase and the disordered phase. Finally, we compare the SPEA method to the sublattice model commonly used in the CALPHAD approach to describe ordered and random solution phases and their transitions. The proposed SPEA model provides a highly efficient approach for modeling defect phase transformations.

Dynamically encircling an exceptional point (EP) in non-Hermitian systems can exploit the intriguing energy topology around the EP, giving rise to non-Hermitian unique applications such as chiral mode switching. In this work, we introduce the concept of EP encirclement to time-reversal-symmetry broken topological systems towards the manipulation of topologically protected one-way edge modes. We design a three-layered non-Hermitian gyromagnetic photonic crystal, which, under specially distributed external magnetic fields, possesses two topological one-way edge modes. The proposed system is found to be equivalent to a two-level non-Hermitian system with an EP at the frequency of interest. We introduce a two-dimensional parameter space to dynamically encircle the EP, where the encircling direction can be switched by parameter designs, while the edge mode direction can be tuned by changing the direction of the magnetic fields. A selective transport of the topological edge modes is realized, that is, the output mode solely depends on the encircling direction, while the output direction depends on the magnetic field. The mode transport behavior is topologically protected such that the performance is robust to local defects and backward scatterings are avoided. Our findings provide a means for manipulating electromagnetic waves in non-Hermitian and topological photonic systems.

In this paper, we present a comprehensive study of magnetic properties of ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$ (CoSnS) crystals using macroscopic characterization and observations of the domain structure (DS) in a wide range of easy- and hard-axis fields $\left(H\right)$ and temperatures $\left(T\right)$. From macroscopic measurements, we derive temperature dependences of the basic magnetic parameters of the material [saturation magnetization $M_s\left(T\right)$, uniaxial anisotropy constant $K\left(T\right)$, and exchange stiffness $A\left(T\right)$] and, based on them, calculate the thermodynamic magnetization $M(H,T)$ curves and DS parameters for pinning-free samples. We find important qualitative and quantitative differences between the theory and experiment defined by the efficient pinning of domain walls (DWs) in our samples. It turns out that, already at temperatures close to the ferromagnetic transition $T_c$, the DW dynamics falls into the heavy creep regime, resulting in a strong deferral of the DS adjustment into the equilibrium state. We suggest that specific magnetic defects, responsible for pinning and causing field-tuned reproducible domain nucleation patterns observed in our high-quality samples, are pointlike. Recently found magnetic polarons formed around vacancies and impurities, which carry strong diamagnetic moments of spin-orbit nature and are intrinsic for CoSnS and expected in other Weyl semimetals, are a possible source of pinning yielding peculiar $M(H,T)$ response of CoSnS.

We identify Floquet exceptional points without a static counterpart, called Floquet $\pi$ exceptional points (FPEPs), whose eigenvectors rotate on the Bloch sphere and accumulate $\pi$ Aharonov-Anandan phase in one time period. The term $\pi$ of FPEPs refers to the Aharonov-Anandan phase of $\pi$ rather than the quasienergy of $\pi$, and an exceptional point with a quasienergy of zero may also be an FPEP. We first show their quasienergy spectral properties and the Aharonov-Anandan phase in a non-Hermitian Floquet two-resonators system. Then we show that they exist in non-Hermitian Floquet bipartite lattices, where there can be an order-1/2 FPEP or an order-1 FPEP. In the lattice model, two order-1/2 FPEPs with same dynamical structure can merge into one order-1 FPEP and the order-1 FPEP appears at the phase transition point between quasimomentum gap phases and quasienergy gap phases. The scattering properties around the order-1 FPEP exhibit perfect transparency but remain detectable in reflection from one of two sides.

We use a single-channel scattering formalism to derive general expressions for the Andreev bound-state energies and resulting current-phase relationship in a one-dimensional semiconductor-based SNS junction, including arbitrarily oriented effective spin-orbit and Zeeman fields and taking into account disorder in the junction in by including a single scatterer with transmission probability $0\le T^2\le 1$, arbitrarily located in the normal region. We first corroborate our results by comparing them to the known analytic limiting-case expressions. Then we simplify our general result in several additional limits, including the case of the scatterer being at a specific location and the cases of small and large spin-orbit fields compared to the Zeeman splitting, assuming low transparency ($T\ll 1$). We believe that our results could be helpful for disentangling the main spin-mixing processes in experiments on low-dimensional semiconductor-based SNS junctions.

We investigate the transport properties of open Josephson junctions (JJs) through a minimal effective non-Hermitian (NH) approach derived from the equilibrium Green's function (GF) formalism. Specifically, we consider a JJ with a quantum dot barrier coupled to a normal metal reservoir. The coupling introduces an imaginary self-energy term in the JJ Hamiltonian which can be naturally accounted for in the NH formalism. While most approaches to similar problems work with the full junction Hamiltonian, we propose a scheme for deriving an effective NH Hamiltonian for the Andreev levels only, which we compute from the singular part of the barrier GF. To establish the range of applicability of this NH model, we benchmark our results for both the dot density of states and the supercurrent against exact GF predictions in different transport regimes. We find that, as a rule of thumb, the Andreev NH description is accurate when the spectral overlap between the Andreev bound states (ABS) and the near-gap continuum states is negligible, i.e., when the ABS energies lie sufficiently far from the superconducting gap relative to their linewidth. This method not only highlights the effective physics of the JJ but also offers a scalable framework for studying large-size devices.

High-$T_c$ cuprates are characterized by strong spin fluctuations, which give rise to antiferromagnetic and pseudogap phases and may be key to the high superconducting critical temperatures observed in these materials. Experimental studies have revealed significant changes in the Hall coefficient $R_H$ across these phases, a phenomenon closely related to both spin fluctuations and changes in the Fermi surface morphology. Utilizing the perturbation correction to Gaussian approximation, the two-dimensional square-lattice single-band Hubbard model is investigated, resulting in the calculation of the self-energy with a finite imaginary part due to scattering. The density dependence of the Hall number, $n_H=1/\left(q{R}_H\right)$, is also calculated. For small hole (or electron) doping $p$ (or $x$), our numerical results demonstrate that $n_H$ transitions from $p$ to $1+p$ for hole-doped systems, and from $-x$ to $1-x$ for electron-doped systems, both in agreement with experimental findings. Furthermore, we discuss the correlation between phase boundaries and the observed peculiar changes in the Hall number.

We present the pressure-temperature phase diagram of Kondo lattice compound $\mathrm{CeAg}{\mathrm{Bi}}_2$ up to 23.4 GPa, which was constructed from electrical resistivity and magnetoresistance measurements. At ambient pressure, an antiferromagnetic phase (labeled AFM-1) below $T_{\mathrm{N}1}=6.4\mathrm{K}$ is observed and four critical fields $H_{\mathrm{C}1}\text{−}{H}_{\mathrm{C}4}$ (3.5, 4.6, 8.1, and 10.1 T) corresponding to successive metamagnetic transitions are identified at 2 K. Combined with synergetic extreme conditions (high pressure and high magnetic field), a different antiferromagnetic phase (labeled AFM-2) is revealed above 1.6 GPa, consistent with results of a previous report. More importantly, $T_{\mathrm{N}2}$ keeps nearly unchanged over a wide pressure range (>15.0 GPa), which is quite unusual. In addition, all metamagnetic transitions observed in the AFM-2 phase are stable under pressure and persist up to the highest studied pressure of 23.4 GPa, which can be ascribed to the magnetic frustration caused by competing anisotropic magnetic interactions. Since the crystalline electric field (CEF) splitting of $\mathrm{CeAg}{\mathrm{Bi}}_2$ is much smaller than its counterparts, the admixture of CEF levels is more likely under pressure, which may be responsible for this robust AFM-2 phase.

We investigate the evolution of magnetic phases in the Hubbard model under strong Rashba spin-orbit coupling on a square lattice. By using Lanczos exact diagonalization and determinant quantum Monte Carlo simulations, we explore the emergence of various magnetic alignments as the ratio between the regular hopping amplitude, $t$, and the Rashba hopping term, $t_R$, is varied over a broad range of Hubbard interaction strengths, $U$. In the limit $t_R\to 0$, the system exhibits Néel antiferromagnetic order, while when $t\sim t_R$, a spiral magnetic phase emerges due to the induced anisotropic Dzyaloshinskii-Moriya interaction. For $t_R>t$, we identify the onset of a spin vortex phase. At the extreme limit $t=0(t_R\ne 0$), we perform finite-size scaling analysis in the Weyl semimetal regime to pinpoint the quantum critical point associated with the spin vortex phase, employing sign-free quantum Monte Carlo simulations—the extracted critical exponents are consistent with a Gross-Neveu-type quantum phase transition.

A recent surge of research on many-body quantum entanglement has uncovered intriguing properties of quantum many-body systems. A prime example is the modular commutator, which can extract a topological invariant from a single wave function. Here, we unveil geometric properties of many-body entanglement via a modular commutator of two-dimensional gapped quantum many-body systems. We obtain the geometric additivity of a modular commutator, which indicates that the modular commutator for a multipartite system may be an integer multiple of the one for tripartite systems. Using our additivity formula, we also derive a curious identity for the modular commutators involving disconnected intervals in a certain class of conformal field theories. We further illustrate this geometric additivity for both bulk and edge subsystems using numerical calculations of the Haldane and $\pi$-flux models.

Recently, it has been shown how topological phases of matter with crystalline symmetry and $U\left(1\right)$ charge conservation can be partially characterized by a set of many-body invariants, the discrete shift ${\mathcal{S}}_{\mathrm{o}}$ and electric polarization ${\vec{\mathcal{P}}}_{\mathrm{o}}$, where $\mathrm{o}$ labels a high-symmetry point. Crucially, these can be defined even with nonzero Chern number and/or magnetic field. One manifestation of these invariants is through quantized fractional contributions to the charge in the vicinity of a lattice disclination or dislocation. In this paper, we show that these invariants can also be extracted from the length and corner dependence of the total charge (mod 1) on the boundary of the system. We provide a general formula in terms of ${\mathcal{S}}_{\mathrm{o}}$ and ${\vec{\mathcal{P}}}_{\mathrm{o}}$ for the total charge of any subregion of the system which can include full boundaries or bulk lattice defects, unifying boundary, corner, disclination, and dislocation charge responses into a single general theory. These results hold for Chern insulators, despite their gapless chiral edge modes, and for which an unambiguous definition of an intrinsically two-dimensional electric polarization has been unclear until recently. We also discuss how our theory can fully characterize the topological response of quadrupole insulators.

In the realm of condensed matter physics, higher-order topological insulators (TIs) and superconductors have become a focal point of research due to their unique gapless boundary states at lower-dimensional boundaries such as corners and edges. This paper delves into the effects of a $d$-density wave (DDW) on first-order TIs and the competitive dynamics between DDW and $d$-wave superconductivity (DSC) within these systems. We demonstrate that a pure DDW state can instigate a transition to a higher-order topological phase, distinct from DSC behavior, as it is influenced by boundary shape and can generate a zero energy corner flat band without additional potentials. However, the introduction of the additional DSC order disrupts this corner flat band, leading to the formation of corner states. Furthermore, we investigate the competitive effects between DSC and DDW, which lead to the transfer of partial corner states. The interplay between these states results by the generation of partial Majorana corner states with different symmetries by proximity-induced DSC, while DDW disrupts these states and creates new corner states at alternative locations. This study provides valuable insights into the manipulation of topological states by competing different order parameters, which could be pivotal for future research and applications in the field.

Recently, the Anderson disorder-induced topological Anderson amorphous insulator has been proposed in a two-dimensional amorphous lattice. However, the interplay between Anderson disorder and amorphous higher-order band topology remains unclear. In this work, we investigate the effects of Anderson disorder on the higher-order topological amorphous phase. We demonstrate that the higher-order topological amorphous phase exhibits robustness against weak disorder but is destroyed by strong disorder. In addition, the Anderson disorder-induced phase transition from a topologically trivial amorphous insulator phase to a higher-order topological amorphous insulator phase, dubbed the higher-order topological Anderson amorphous insulator, is characterized by a quantized quadrupole moment and the existence of topological corner states. Our findings may greatly enrich the study of the interplay between disorder and higher-order topology in amorphous systems and add a new dimension to the topological states of matter.

Topological corner states have been extensively studied in two-dimensional (2D) topological insulators (TIs), yet they remain rarely reported in 2D magnetic metal-organic frameworks (MOFs). In this work, we uncover the nontrivial corner states protected by $C_{2z}$ and $C_{4z}$ symmetry in three 2D ferrimagnetic MOFs. In the ferrimagnetic ${\mathrm{Cr}\left(\mathrm{ODZ}\right)}_2$ (DZ = 1.2.5-diazole) with a magnetic space group (MSG) 14.2.87, the occupied electronic bands contain the essential band representations (BRs) of $A_u@2b$ and $A_g@2c$ with unconventional features, facilitating the formation of quantized fractional charge $\left(\frac{e}{2}\right)$ in both spin-up and spin-down channels under $C_{2z}$ symmetry protection. Even in the presence of spin-orbit coupling (SOC), these nontrivial corner states are well preserved. Additionally, the $C_{4z}$ symmetry protected corner states are also identified in two other types of ferrimagnetic MOFs, specifically, ${\mathrm{Cr}\left(\mathrm{SDZ}\right)}_2$ and ${\mathrm{Cr}\left(\mathrm{SeDZ}\right)}_2$ monolayers in MSG 100.5.840 in the presence of SOC, contributed by the following basic BRs: $A_u@2b+A_g@2d$. In the former, the magnetic corner states only exist in the spin-up channel, whereas in the latter, they are present in both spin-up and spin-down channels. Our research findings offer an ideal material platform for exploring the application of magnetic corner states in a special topological device.

In recent years, two-dimensional twisted systems have gained increasing attention. However, calculating the electronic structures in twisted materials has remained a challenge. To address this, we have developed a general computational methodology that can generate twisted geometries starting from a monolayer structure and obtain a precisely relaxed twisted structure through a machine learning-based method. Then, the electronic structure properties of the twisted material are calculated using the tight-binding (TB) and continuum model methods; thus, the entire process requires minimal computational resources. We introduce the theoretical methods for generating twisted structures and computing their electronic properties, and further provide calculations and brief analyses of the electronic structure properties for several typical two-dimensional materials with different characteristics. This paper serves as a solid foundation for researchers interested in studying twisted systems.

The Fermi-edge singularity in x-ray absorption spectra of metals is a paradigmatic case of a logarithmically divergent perturbation series. Prior work has thoroughly analyzed the leading logarithmic terms. Here, we investigate the perturbation theory beyond leading logarithms and formulate self-consistent equations to incorporate all leading and next-to-leading logarithmic terms. This parquet solution of the Fermi-edge singularity goes beyond the previous first-order parquet solution and sheds new light on the parquet formalism regarding logarithmic behavior. We present numerical results in the Matsubara formalism and discuss the characteristic power laws. We also show that, within the single-boson exchange framework, multi-boson exchange diagrams are needed already at the leading logarithmic level.

Motivated by the three-dimensional structure of Kitaev materials we explore multilayer Kitaev models. The magnetic properties of a multilayer with an arbitrary number of Kitaev honeycomb layers stacked on top of each other coupled through a Heisenberg interaction $J$ is analyzed through Abrikosov fermion mean-field theory. We find quantum spin liquid (QSL) solutions which are gapped (ungapped) for even (odd) number of layers. The presence (absence) of the gap in even- (odd-) layered systems is associated with the spontaneous breaking (nonbreaking) of the inversion symmetry of the multilayer by the mean-field QSL solution. The good agreement between the Gutzwiller projected mean-field energy and the exact energy at large $J$ indicates that our QSL solution is adiabatically connected to the exact ground state. We also find that the Kitaev gapped chiral quantum spin liquid induced by external magnetic fields is stabilized by an antiferromagnetic interlayer coupling. Our results are relevant to the physics of $\alpha \text{−}{\mathrm{RuCl}}_3$ and ${\mathrm{H}}_3{\mathrm{LiIr}}_2{\mathrm{O}}_6$ which are examples of magnetically coupled multilayer Kitaev models.