We describe a numerical approach to modeling magnetoelectric effects generated by spin-orbit coupling in inhomogeneous diffusive two-dimensional (2D) superconductors. It is based on direct minimization of the free energy of diffusion modes, including their coupling to the spin-orbit field strength, described by a recently discovered $\sigma$-model action. We explain how to retain exact conservation laws in the the discretized model, and detail the numerical procedure. We apply the approach to the spin-galvanic and the inverse spin-galvanic effects in finite-size 2D superconductors, and describe short-range oscillations of circulating currents and spin densities originating from the spin-orbit coupling.

Topological semimetals are some of the topological phases of matter most intensely studied experimentally. The Weyl semimetal phase, in particular, has garnered tremendous, sustained interest given fascinating signatures such as the Fermi arc surface states and the chiral anomaly, as well as the minimal requirements to protect this three-dimensional (3D) topological phase. Here, we show that thin films of Weyl semimetals [which we call quasi-($3-1$)-dimensional, or q($3-1$)D] generically realize finite-size topological phases distinct from 3D and 2D topological phases of established classification schemes: response signatures of the 3D bulk topology coexist with topologically protected, quasi-($3-2$)D Fermi arc states or chiral boundary modes due to a second, previously unidentified bulk-boundary correspondence. We show these finite-size topological semimetal phases are realized by Hamiltonians capturing the Fermiology of few-layer van der Waals material ${\mathrm{MoTe}}_2$ in experiment. Given the broad experimental interest in few-layer van der Waals materials and topological semimetals, our work paves the way for extensive future theoretical and experimental characterization of finite-size topological phases.

A deep understanding of the mechanisms underlying many-body quantum chaos is one of the big challenges in contemporary theoretical physics. We tackle this problem in the context of a set of perturbed quadratic Sachdev-Ye-Kitaev (SYK) Hamiltonians defined on graphs. This allows us to disentangle the geometrical properties of the underlying single-particle problem and the importance of the interaction terms, showing that the former is the dominant feature ensuring the single-particle to many-body chaotic transition. Our results are verified numerically with state-of-the-art numerical techniques, capable of extracting eigenvalues in a desired energy window of very large Hamiltonians. Our approach essentially provides a new way of viewing many-body chaos from a single-particle perspective.

Intriguing phenomenon of dimensional crossover is comprehensively studied by experimental and theoretical investigation of the electronic structure in quasi-one-dimensional hollandite ${\mathrm{K}}_2{\mathrm{Ru}}_8{\mathrm{O}}_{16}$. Valence band photoemission spectra in conjunction with density functional theory within local density approximation combined with dynamical mean field theory ($\text{LDA}+\text{DMFT}$) reveal moderately correlated electronic structure. Anomalous temperature dependence of high-resolution spectra in the vicinity of Fermi level suggests Tomonaga-Luttinger liquid state down to 150 K, below which it undergoes a dimensional crossover from one-dimensional to three-dimensional electronic behavior. Monotonously decreasing spectral intensity at the Fermi level along with Fermi cutoff at low temperature suggests non-Fermi liquid like behavior. Many-body effects captured within $\text{LDA}+\text{DMFT}$ reveal increased warping of the Fermi surface with lowering temperature. A simple analysis suggests that the warping dominates the thermal energy induced momentum broadening at low temperature, leading to the three-dimensional electronic behavior. Our results offer valuable insight into understanding the interplay of dimensionality, electron correlation, and thermal energy governing various exotic phenomena in quasi-one-dimensional systems.

Spatially modulated symmetries have emerged since the discovery of fractons, which characterize unconventional topological phases with mobility-constrained quasiparticle excitations. On the other hand, noninvertible symmetry operators have attracted substantial attention in communities of high energy and condensed matter physics due to their deep insight into quantum anomalies and exotic phases of matter. However, the connection between these exotic and noninvertible symmetries has not been fully explored. In this paper, we construct concrete lattice models with noninvertible symmetry operators via gauging spatially modulated symmetries and investigate their exotic fusion rules. Specifically, we construct spin models with subsystem symmetries or dipole symmetries on one, two, and three-dimensional lattices. Gauging subsystem symmetries leads to noninvertible symmetry operators whose fusion rules involve 0-form subsystem charges in two dimensions and higher-form operators that correspond to “lineon” excitations (excitations which are mobile along one-dimensional line) in three dimensions. Gauging dipole symmetries leads to noninvertible symmetry operators with dipole algebras that describe a hierarchical structure between global and dipole charges. Notably, the hierarchical structure of the dual dipole charges is inverted compared with the original ones. Our work provides a unified and systematic analytical framework for constructing exotic symmetry operators by gauging relevant symmetries.

We have developed an analytical expression for $s$-state exciton energies in monolayer transition metal dichalcogenides (TMDCs) as $E_{ns}=-{\text{Ry}}^{*}\times P_n/{(n-0.5+0.479r_0^{*}/\kappa )}^2, n=1,2,3,...$ within the perturbation theory. Here, $r_0^{*}$ and $\kappa$ represent the dimensionless screening length and the surrounding medium's dielectric constant, respectively; ${\text{Ry}}^{*}$ is an effective Rydberg energy scaled by the dielectric constant and exciton reduced mass; $P_n(r_0^{*}/\kappa )$ is a function of variables $n$ and $r_0^{*}/\kappa$ with values around 1.0, so it is considered a term that corrects the Rydberg energy. Despite the simple form, the suggested formula provides exciton energies with high precision compared to the exact numerical solutions and accurately describes recent experimental data for TMDC materials such as ${\mathrm{WSe}}_2, {\mathrm{WS}}_2, {\mathrm{MoSe}}_2, {\mathrm{MoS}}_2$, and ${\mathrm{MoTe}}_2$ encapsulated by hexagonal boron nitride. To achieve these results, we have developed a regulated perturbation theory by combining the conventional perturbation method with several elements of the Feranchuk-Komarov operator method. These include the Levi-Civita transformation, the algebraic calculation technique using the annihilation and creation operators, and the introduction of a free parameter to optimize the convergence rate of the perturbation series. This analytical form of exciton energies, working well in the range $1.45>r_0^{*}/\kappa >0.65$, covers a large class of TMDC monolayers and could be beneficial in various physical analyses, including retrieval of the material parameters such as reduced exciton mass and screening length from the available measured exciton energies.

Sliding ferroelectricity and band topology are two fundamental phenomena in condensed matter physics that offer significant potential for both scientific exploration and technological applications. Here, based on first-principles, we show that the prototypical ${\mathrm{Bi}}_2{\mathrm{Te}}_3/\mathrm{Mn}{\mathrm{Bi}}_2{\mathrm{Te}}_4$ heterobilayer supports the coexistence of sliding ferroelectricity and topological insulating states. Importantly, under appropriate external strain, the two nonequivalent ferroelectric (FE) states can exhibit distinct topological phases, enabling sliding FE control of the topological state. The explored findings not only provide foundations for exploring emergent phenomena and potential applications in ${\mathrm{Bi}}_2{\mathrm{Te}}_3/\mathrm{Mn}{\mathrm{Bi}}_2{\mathrm{Te}}_4$ but also contribute to ongoing research on sliding ferroelectricity and topological insulating states at the heterointerfaces.

Bound states in the continuum (BICs) have attracted significant attention due to their intriguing properties. The introduction of square-root topology often leads to multifrequency topological bound states, enhancing the richness of the system behavior. In this study, we construct a square-root topological circuit hosting topological bound states in multi-frequency gaps based on connected double Su-Schrieffer-Heeger chains. By simple adjustments, the double chains can be decoupled, transitioning into square-root topological bound states in the continuum circuit (STBICs). Experimental validations are conducted to confirm the coexistence of both topological and trivial bound states in these systems. Furthermore, we demonstrate robustness against perturbations, providing strong evidence supporting the topological protection of BICs. Our research bridges the gap between square-root topology and BICs, resulting in rich topological properties and offering insight into the potential applications of square-root topological BICs circuits.

Thermal broadening of the quasiparticle peak in the spectral function is an important physical feature in many statistical systems, but it is difficult to calculate. To tackle this problem, we propose the $H$-expanded basis within the projective truncation approximation (PTA) of the Green's function equation of motion. A zeros-removing technique is introduced to stabilize the iterative solution of the PTA equations. Benchmarking calculations on the classical one-variable anharmonic oscillator model and the one-dimensional ${\varphi }^4$ lattice model show that the thermal broadened quasiparticle peak in the spectral function can be produced on a semiquantitative level. Using this method, we discuss the low- and high-temperature power-law behaviors of the spectral width ${\mathrm{\Gamma }}_k\left(T\right)$ of the one-dimensional ${\varphi }^4$ model, finding it in contradiction with the assumption of effective phonon theory. A short-chain limit of this model is also discovered. Issues of extending the $H$-expanded basis to quantum systems and of the applicability of the Debye formula for thermal conductivity are discussed.

The antiferromagnetic sawtooth chain is a prototypical example of a frustrated spin system with vertex-sharing triangles, giving rise to complex quantum states. Depending on the interaction parameters, this system has three phases, of which the gapless noncollinear phase (for strongly coupled basal spins and loosely attached apical spins) has received little theoretical attention so far. In this work, we comprehensively investigate the properties of the noncollinear phase using large-scale tensor network computations which exploit the full SU(2) symmetry of the underlying Heisenberg model. We study the ground state both for finite systems using the density-matrix renormalization group (DMRG) as well as for infinite chains via the variational uniform matrix-product state (VUMPS) formalism. Finite temperatures and correlation functions are tackled via imaginary or real time evolutions, which we implement using the time-dependent variational principle (TDVP). We find that the noncollinear phase is characterized by a low-momentum peak and a diffuse tail for the apex-apex correlations. Deep into the phase, the pattern sharpens into a peak indicating a ${90}^{\circ }$ spiral. The apical spins are soft and highly susceptible to external perturbations; they give rise to a large number of gapless magnetic states that are polarized by weak fields and cause a long low-temperature tail in the specific heat. The dynamic spin-structure factor exhibits additive contributions from a two-spinon continuum (excitations of the basal chain) and a gapless peak at $k=\pi /2$ (excitations of the apical spins). Small temperatures excite the gapless states and smear the spectral weight of the $k=\pi /2$ peak out into a homogeneous flat-band structure. Our results are relevant, e.g., for the material atacamite ${\mathrm{Cu}}_2\mathrm{Cl}{\left(\mathrm{OH}\right)}_3$ in high magnetic fields.

Loop current order has been suggested as a promising candidate for the spontaneous time-reversal symmetry breaking $2a_0\times 2a_0$ charge density wave (CDW) revealed in vanadium-based kagome metals $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ ($A=\mathrm{K},\mathrm{Rb},\mathrm{Cs}$) near van Hove filling $n_{\text{vH}}=\frac{5}{12}$. Weak-coupling analyses and mean field calculations have demonstrated that nearest-neighbor Coulomb repulsion $V_1$ and next-nearest-neighbor Coulomb repulsion $V_2$ drives, respectively, real and imaginary bond-ordered CDW, with the latter corresponding to time-reversal symmetry-breaking loop current CDW. It is important to understand the interlayer correlation of these bond-ordered CDWs and its consequences in the bulk kagome materials. To provide physical insights, we investigate in this paper the $c$-axis stacking of them, loop current CDW in particular, on the minimal bilayer kagome lattice. The bare susceptibilities for stacking of real and imaginary bond orders are calculated for the free electrons on the bilayer kagome lattice with interlayer coupling $t_{\perp }=0.2t$, which splits the van Hove filling to $n_{+\text{vH}}=4.64/12$ and $n_{-\text{vH}}=5.44/12$. While real and imaginary bond-ordered CDWs are still favored, respectively, by $V_1$ and $V_2$, their interlayer coupling is sensitive to band filling $n$. They tend to stack symmetrically near $n_{\pm \text{vH}}$ with identical bond orders in the two layers and give rise to a $2a_0\times 2a_0\times 1c_0$ CDW. On the other hand, they prefer to stack antisymmetrically around $n_{\text{vH}}$ with opposite bond orders in the two layers and lead to a $2a_0\times 2a_0\times 2c_0$ CDW. The concrete bilayer $t\text{−}{t}_{\perp }\text{−}{V}_1\text{−}{\mathrm{V}}_2$ model is then studied. We obtain the mean field ground states and determine the interlayer coupling as a function of band filling at various interactions. The nontrivial topological properties of loop current CDWs are studied and possible connections to experiments are discussed.

In this paper, we propose a transmission dip in a terahertz (THz) metamaterial device by employing the coupling between bright mode and interference of dark modes. We provide the theoretical analysis, analytical calculations, and simulations to present the transmission spectrum of metamaterials. Furthermore, we observe the tendency of the transmission spectrum through experiments, which effectively verify our idea. Ideally, this transmission dip can produce a very high-Q peak in the middle of the transmission spectrum of electromagnetically induced transparency (EIT), which can be useful for highly sensitive metamaterial sensors, optical switches, and photomemory.

Band structures of electrons in a periodic potential are well-known to host topologies that impact their behaviors at edges and interfaces. The concept however is more general than the single-electron setting. In this work, we consider topology of plasmons in a two-dimensional metal, subject to a unidirectional periodicity. We show how the plasmon modes and wave functions may be computed for such a periodic system, by focusing on the confined, quantized photon degrees of freedom associated with the plasmon modes. At low frequencies the plasmons disperse with wave vector as $\sqrt{q}$; however at higher frequencies one finds a series of bands and gaps in the spectrum. For a unidirectional periodic electron density with inversion symmetry, we show that each band hosts a Zak phase ${\gamma }_n$ which may only take the values 0 or $\pi$. Each gap has a topological index $\nu$ that is determined by the sum of the Zak phases below it. When the system has an interface with the vacuum, one finds in-gap modes for gaps with nontrivial topologies, which are confined to the interface. In addition, interfaces between systems that are the same except for their topologies—which can be created by a defect in the lattice in which half a unit cell has been removed—host in-gap, confined states when the topological indices of the relevant gaps are different. We demonstrate these properties numerically by analyzing a Kronig-Penney-type model in graphene, in which the electron density is piecewise constant, modulating between two different densities. In addition, we consider a related plasmon system modeled after the Su-Schrieffer-Heeger (SSH) model. We show that the topological phase diagram of the lowest energy bands is highly analogous to that of the SSH tight-binding system.

The interplay between topological localization and non-Hermiticity localization in non-Hermitian crystal systems results in a diversity of shapes of topological edge modes (EMs), offering opportunities to manipulate these modes for potential topological applications. The characterization of the domain of EMs and the engineering of these EMs require detailed information about their wave function, which conventional calculation of topological invariants cannot provide. In this Letter, by recognizing EMs as specified solutions of an eigenequation, we derive their wave functions in an extended non-Hermitian Su-Schrieffer-Heeger model. We then inversely construct a winding tuple $\{w_{\text{GBZ}},w_{\text{BZ}}\}$ that characterizes the existence of EMs and their spatial distribution. Moreover, we define a spectral winding number equivalent to $w_{\text{BZ}}$, which is determined by the product of energies of different bands. The inverse design of topological invariants allows us to categorize the localized nature of EMs even in systems lacking sublattice symmetry, which can facilitate the manipulation and utilization of EMs in the development of different quantum materials and devices.

The paper presents ab initio calculations taken to study the electronic structure, phonon spectrum, and electron-phonon coupling factor $G(T_e$) of several metals (Ag, Au, Pd, Pt, Rh, Ir, W, and Ta) at different electron temperatures $T_e$ ($\sim {10}^4\mathrm{K}$) and “cold” crystal lattice. We studied the effect of changes in the electronic structure under electron heating on lattice dynamics and the electron-phonon coupling factor. The outcomes of our study suggest that the evolution of lattice dynamics is quite well correlated with changes in the electronic population of the outer d bands with the growing $T_e$. The decrease in the number of d electrons results in crystal hardening because the Coulomb potential screening of nuclei reduces, while their increase leads to the growth of the electronic screening and lattice softening. Our calculations show that in the initial phase of heating ($T_e<20$ kK), the increase of the electron temperature in fcc metals may result in both lattice hardening (Pd, Pt) and softening (Rh, Ir), or quite weak changes in lattice dynamics (Ag, Au). However, lattice softening never makes fcc metals lose their dynamic stability. At higher temperatures ($T_e>20$ kK), the tendency to lattice hardening always prevails in them. As for the bcc metals, they are found to lose their dynamic stability as the electron temperature increases above 20 kK. It is also shown in this paper that differences in the electronic structures of metals strongly influence the behavior of the electron-phonon coupling factor as dependent on the electron temperature.

We study the effect of diluting a two-dimensional ferromagnetic insulator hosting a topological phase in the clean limit. By considering the ferromagnetic Heisenberg model in the honeycomb lattice with second-nearest-neighbor Dzyaloshinskii-Moriya interaction, and working in the linear spin-wave approximation, we establish the topological phase diagram as a function of the fraction $p$ of diluted magnetic atoms. The topological phase with Chern number $C=1$ is robust up to a moderate dilution $p_1^{*}$, while above a higher dilution $p_2^{*}>p_1^{*}$ the system becomes trivial. Interestingly, both $p_1^{*}$ and $p_2^{*}$ are below the classical percolation threshold $p_c$ for the honeycomb lattice, which gives physical significance to the obtained phases. In the topological phase for $p<p_1^{*}$, the magnon spectrum is gapless but the states filling the topological, clean-limit gap region are spatially localized. For energies above and below the region of localized states, there are windows composed of extended states. This is at odds with standard Chern insulators, where extended states occur only at single energies. For dilutions $p_1^{*}<p<p_2^{*}$, the two regions of extended states merge and a continuum of delocalized states appears around the middle of the magnon spectrum. For this range of dilutions the Chern number seems to be ill defined in the thermodynamic limit, and only for $p>p_2^{*}$, when all states become localized, the system shows $C=0$ as expected for a trivial phase. Replacing magnetic with nonmagnetic atoms in a system hosting a magnon Chern insulator in the clean limit puts all the three phases within experimental reach.

The non-Hermitian skin effect (NHSE) is a distinctive topological phenomenon observed in non-Hermitian systems. Recently, there has been considerable interest in exploring higher-order NHSE occurrences in two and three dimensions. In such systems, topological edge states collapse into a corner while bulk states remain delocalized. Through a Hermitian–non-Hermitian correspondence, this study predicts and experimentally observes the higher-order NHSE in an acoustic kagome lattice possessing nonreciprocal hoppings. By rotating the frequency spectrum and employing complex-frequency excitation techniques, we observe the localization of acoustic energy towards a corner of the lattice in the topologically nontrivial phase, even when the source is located far from that corner. In contrast, the acoustic energy spreads out when excited at the frequencies hosting the bulk states. These observations are unequivocal evidence of the higher-order NHSE.

We analyze modes in a dipole-dipole coupled quantum Ising material, taking into consideration shape effects present in any real magnet. We find that the soft mode governing quantum criticality in a nonellipsoidal sample is a magnetostatic mode that nulls out the effects of dynamic-demagnetization-field fluctuations. The demagnetization field is analyzed from a microscopic perspective. Two additional modes are calculated relying solely on knowledge of the demagnetization factor of the sample, one of which has lower energy than the soft mode governing quantum criticality in the bulk of the magnet. Experimental evidence for these theoretical results is provided by analysis of electronuclear modes in ${\mathrm{LiHoF}}_4$, an archetypal quantum Ising material.