We investigate a two-level topological system with an alternating XX coupling in a photon cavity. It is mapped to a free boson model equally coupled to a photon, whose interaction is highly nonlocal. We analyze the Su-Schrieffer-Heeger model and the breathing kagome model. Intriguing phenomena occur in the topological phase due to hybridization between the photon field and the topological edge or corner state. As the photon coupling increases, the symmetric edge or corner state is smoothly transformed into a polariton state coupled with the edge or corner state. Simultaneously, the photon state is smoothly transformed into the symmetric edge state or the ${\mathrm{C}}_{\text{3}}$-symmetric corner state. Furthermore, a state is detached from the bulk band and smoothly transformed into a polariton due to hybridization with the photon field.

We investigate numerically how on-site disorder affects conduction in the periodically driven Rice-Mele model, a prototypical realization of the Thouless pump. Although the pump is robust against disorder in the fully adiabatic limit, much less is known about the case of finite period time $T$, which is relevant also in light of recent experimental realizations. We find that, at any fixed period time and nonzero disorder, increasing the system size $L\to \infty$ always leads to a breakdown of the pump, indicating Anderson localization of the Floquet states. Our numerics indicate, however, that, in a properly defined thermodynamic limit, where $L/T^{\theta }$ is kept constant, Anderson localization can be avoided, and the charge pumped per cycle has a well-defined value — as long as the disorder is not too strong. The critical exponent $\theta$ is not universal, rather, its value depends on the disorder strength. Our findings are relevant for practical, experimental realizations of the Thouless pump, for studies investigating the nature of its current-carrying Floquet eigenstates, as well as the mechanism of the full breakdown of the pump, expected if the disorder exceeds a critical value.

The nonequilibrium steady states of quantum materials have many challenges. Here, we highlight issues with the relaxation time approximation (RTA) for the dc conductivity in insulating systems. The RTA to the quantum master equation (QME) is frequently employed as a simple method, yet this phenomenological approach is exposed as containing a fatal flaw, displaying non-negligible dc conductivity in the linear response regime. We find that the puzzling behavior is caused by the fact that the density matrix in the RTA incompletely incorporates the first order of the external field. To solve this problem, we have derived a calculation scheme based on the QME that ensures correct behavior in low electric fields. Our method reproduces well the overall features of the exact electric currents in the whole field region. It is not time consuming, and its application to lattice systems is straightforward. This method will encourage progress in this research area as a simple way to more accurately describe nonequilibrium steady states.

We study thermal transport and thermalization in single crystals of ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ through the CDW transition by directly measuring thermal diffusivity ($D$), thermal conductivity ($\kappa$), specific heat ($c$), and resistivity ($\rho$). Commensurate with previous reports, we observe a sharp, narrow anomaly in specific heat associated with a first-order transition that results in a CDW state below $\sim 94$ K. While a corresponding sharp anomaly in thermal diffusivity is also observed, resistivity and thermal conductivity only exhibit small steps at the transition, where the feature is sharp for resistivity and broader for thermal conductivity. Scrutinizing the thermal Einstein relation $\kappa =cD$, we find that this relation is generally satisfied, except in the narrow two-phase regime of the putative first-order transition. The Wiedemann-Franz law as well seems to work outside the two-phase regime, where strong resemblance between the specific heat and the resistivity derivative below the transition may point to a concurrent emergence of a secondary electronic order parameter.

Although it is recognized that Anderson localization takes place for all states at a dimension $d$ less than or equal to 2, while delocalization is expected for hopping $V\left(r\right)$ decreasing with the distance slower or as $r^{-d}$, the localization problem in the crossover regime for the dimension $d=2$ and hopping $V\left(r\right)\propto r^{-2}$ is not resolved yet. Following earlier suggestions we show that for the hopping determined by two-dimensional anisotropic dipole-dipole interactions in the presence of time-reversal symmetry there exist two distinguishable phases at weak and strong disorder. The first phase is characterized by ergodic dynamics and superdiffusive transport, while the second phase is characterized by diffusive transport and delocalized eigenstates with fractal dimension less than 2. The transition between phases is resolved analytically using the extension of scaling theory of localization and verified numerically using an exact numerical diagonalization.

We report neutron diffraction results for the body-centered-tetragonal series $\mathrm{Eu}{\left({\mathrm{Co}}_{1-x}{\mathrm{Ni}}_x\right)}_{2-y}{\mathrm{As}}_2, x=0.10$, 0.20, 0.42, and 0.82, $y\le 0.10$, that detail changes to the magnetic ordering with nominal hole doping. We report the antiferromagnetic (AFM) propagation vectors, magnetic transition temperatures, and the ordered magnetic moments. We find a nonmonotonic change of the AFM propagation vector with $x$, with a minimum occurring at the tetragonal to collapsed-tetragonal phase crossover. For $x=0.10$ and 0.82 we find $c$-axis helix ordering of the Eu magnetic moments (spins) similar to $x=0$ and 1, with the spins oriented within the $\mathbf{ab}$-plane. For $x=0.20$ and 0.42 we find higher-temperature $c$-axis ferromagnetic (FM) order and lower-temperature $c$-axis cone order. Using the extinction conditions for the space group, we discovered that the Eu spins are ordered in the higher-temperature $c$-axis FM phase for intermediate values of $x$, contrary to a previous report suggesting only Co/Ni spin ordering. Although we cannot directly confirm that the Co/Ni spins are also ordered, we suggest that $c$-axis itinerant-FM ordering of the Co/Ni spins could provide a molecular field that drives FM ordering of the Eu spins, which in turn provides the anisotropy for the lower-temperature $c$-axis cone order.

We report comparative study of ferromagnetic properties in non-Heisenberg 1/1 and 2/1 approximant crystals (ACs) with close chemical compositions in the quinary Au-Cu-Al-In-Tb alloy system. The 1/1 and 2/1 ACs exhibit comparable Weiss temperatures $[{\theta }_{\mathrm{w}}=+17.8\left(5\right)\mathrm{and}+14.6\left(5\right)\mathrm{K}]$, Curie temperatures ($T_{\mathrm{C}}=15.8$ and 14.3 K), and magnetic entropy changes $\left(\mathrm{\Delta }{S}_M\right)$ under 5 T magnetic field change (−3.8 and −3.7 J/K mol Tb), respectively, showing insignificant role of the AC degree in the magnetism of the non-Heisenberg ACs. Moreover, the magnetic behavior of the quinary 1/1 AC is almost identical to that of the ternary ${\mathrm{Au}}_{64}{\mathrm{Al}}_{22}{\mathrm{Tb}}_{14}$ 1/1 AC [N. Kikugawa, et al., J. Alloys Compd. 882, 160669 (2021).], which implies that chemical disorder introduced in the quinary 1/1 AC does not appreciably affect the ferromagnetic behavior, pointing toward the dominant magnetic interactions on a shorter length scale. The comparable magnetic behaviors between the 1/1 and 2/1 ACs are partly understood in terms of the similar distribution profiles of the interspin distances, up to third-nearest neighbor interactions, well beyond the common icosahedral cluster.

We consider an antiferromagnetic four-leg spin-1/2 tube using Abelian and non-Abelian bosonization. We show that in the limit of weak interchain coupling, the most relevant interaction gives rise to an emergent $\mathrm{SU}\left(3\right)$ symmetry, broken only by marginal interactions that can be canceled by diagonal interchain couplings. We discuss the low-energy spectrum in the semiclassical limit and using a mapping to a trimerized $\mathrm{SU}\left(3\right)$ spin chain. We establish that the correlation functions of ferroquadrupolar operators can be used to reveal the emergent symmetry.

Epitaxial strain has emerged as a powerful tool to tune magnetic and ferroelectric properties in functional materials such as in multiferroic perovskite oxides. Here, we use first-principles calculations to explore the evolution of magnetic interactions in the antiferromagnetic (AFM) multiferroic ${\mathrm{BiFeO}}_3$ (BFO), one of the most promising multiferroics for future technology. The epitaxial strain in BFO(001) oriented film is varied between ${\varepsilon }_{xx,yy}\in [-2\%,+2\%]$. We find that both strengths of the exchange interaction and Dzyaloshinskii-Moriya interaction decrease linearly from compressive to tensile strain whereas the uniaxial magnetocrystalline anisotropy follows a parabolic behavior which lifts the energy degeneracy of the (111) easy plane of bulk BFO. From the trends of the magnetic interactions we can explain the destruction of cycloidal order in compressive strain as observed in experiments due to the increasing anisotropy energy. For tensile strain, we predict that the ground state remains unchanged as a function of strain. By using the domain wall energy, we envision the region where isolated chiral magnetic textures might occur as a function of strain, i.e., where the collinear AFM and the spin spiral energies are equal. This transition between $-1.5$ and $-0.5\%$ of strain should allow topologically stable magnetic states such as antiferromagnetic skyrmions and/or merons to occur. Hence, our paper should trigger experimental and theoretical investigations in this range of strain.

One of the fundamental facts of condensed matter physics is that sufficient amount of disorder always turns a Fermi-liquid metal into an Anderson insulator: a compressible but nonconducting phase of matter. Recently, topological semimetals have emerged as another way a metallic phase may be realized. In this paper we point out that, unlike ordinary metals, at least some topological semimetals are immune to localization, provided certain conditions are satisfied. We present several physical arguments, based on diagrammatic perturbation theory and Keldysh field theory, as well as decorated domain wall construction, to back up this claim.

Single- and two-particle spectra of a single immobile impurity immersed in a fermionic bath can be computed exactly and are characterized by divergent power laws (edge singularities). Here we present the leading lattice correction to this canonical problem by embedding both impurity and bath fermions in bands with nonvanishing Bloch band geometry, with the impurity band being flat. By analyzing generic Feynman diagrams, we pinpoint how the band geometry reduces the effective interaction which enters the power laws; we find that for weak lattice effects or small Fermi momenta, the leading correction is proportional to the Fermi energy times the sum of the quantum metrics of the bands. When only the bath fermion geometry is important, the results can be extended to large Fermi momenta and strong lattice effects and cross-validated by analysis of $S$-matrix eigenvalues. We numerically illustrate our results on the Lieb lattice and draw connections to various spectroscopy experiments.

The nuclear spin systems in CdTe/(Cd,Zn)Te and CdTe/(Cd,Mg)Te quantum wells (QWs) are studied using a multistage technique combining optical pumping and Hanle effect-based detection. The samples demonstrate drastically different nuclear spin dynamics in zero and weak magnetic fields. In CdTe/(Cd,Zn)Te, the nuclear spin relaxation time is found to strongly increase with the magnetic field, growing from 3 s in zero field to tens of seconds in a field of 25 G. In CdTe/(Cd,Mg)Te the relaxation is an order of magnitude slower, and it is field-independent up to at least 70 G. The differences are attributed to the nuclear spin relaxation being mediated by different kinds of resident electrons in these QWs. In CdTe/(Cd,Mg)Te, a residual electron gas trapped in the QW largely determines the relaxation dynamics. In CdTe/(Cd,Zn)Te, the fast relaxation in zero field is due to interaction with localized donor-bound electrons. Nuclear spin diffusion barriers form around neutral donors when the external magnetic field exceeds the local nuclear field, which is about $B_L\approx 0.4$ G in CdTe. This inhibits nuclear spin diffusion towards the donors, slowing down relaxation. These findings are supported by theoretical modeling. In particular, we show that the formation of the diffusion barrier is made possible by several features specific to CdTe: (i) the large donor binding energy (about 10 meV), (ii) the low abundance of magnetic isotopes (only $\approx 30$% of nuclei have nonzero spin), and (iii) the absence of nuclear quadrupole interactions between nuclei. The two latter properties are also favorable to nuclear spin cooling via optical pumping followed by adiabatic demagnetization. Under nonoptimized conditions we have reached sub-microkelvin nuclear spin temperatures in both samples, lower than all previous results obtained in GaAs.

The puckered lattice geometry, along with $p$ orbitals, is often overlooked in the study of topological physics. Here, we investigate the higher-order topology of the $p_{x,y}$-orbital bands in acoustic metamaterials using a simplified two-dimensional phosphorene lattice which possesses a puckered structure. Notably, unlike the $s$-orbital bands in planar lattices, the unique higher-order topology observed here is specific to $p$ orbitals and the puckered geometry due to the unusual hopping patterns induced by them. Using acoustic pump-probe measurements in metamaterials, we confirm the emergence of the edge and corner states due to the unconventional higher-order topology. We reveal the uniqueness of the higher-order topological physics here via complimentary tight-binding calculations, finite-element simulations, and acoustic experiments. We analyze the underlying physics of the special properties of the edge and corner states in the puckered lattice acoustic metamaterials from the picture of Wannier orbitals. Our work sheds light on the intriguing physics of $p$-orbital topological physics in puckered lattices and acoustic metamaterials which lead to unconventional topological boundary states.

Recent studies on the interplay between band topology and the layer degree of freedom provide an effective way to realize exotic topological phases. Here we systematically study the $C_6$- and $C_3$-symmetric higher-order topological phases in bilayer spinless tight-binding lattice models. For concreteness, we consider bilayer phononic crystals as the realizations of these models. We find that for mirror-symmetric-stacking bilayer lattices the interlayer couplings control the emergence and disappearance of the topological bound states in the continuum where we consider the corner states as possible bound states in the bulk continuum. For the bilayer phononic crystals formed by two different lattices with identical symmetry, the band topology is determined by both the band topology of each layer as well as their mutual couplings. The bilayer phononic crystals experience various topological phase transitions when the interlayer couplings are gradually increased. Our paper reveals the rich physics and topological phases emerging in bilayer lattice systems that can be used to engineer interesting phenomena and topological effects.

There have been numerous studies on topological superconductivity in magnetic atomic chains deposited on $s$-wave superconductors. Most of these investigations have focused on spin-orbit interactions or helical spin orders. In this paper, we propose a model for achieving one-dimensional topological superconductivity in a magnetic atomic ring. This model utilizes a magnetic field and an antiferromagnetic/ferromagnetic order, under the condition that the magnetic field is perpendicular to the moments of the magnetic order. On a quasi-one-dimensional substrate surface, where the half-filled ring favors an antiferromagnetic configuration, we demonstrate that either the magnetic field itself or a Rashba spin-orbit coupling guarantees the perpendicularity. On a two-dimensional surface, where the ring favors ferromagnetic orders, the perpendicularity is achieved by introducing a minor Rashba spin-orbit coupling.

The experimental investigations of the magnetic interactions in an atomically thin magnetic layer are essential to understand the physics of low-dimensional magnets. The dispersion relation of collective magnetic excitations (magnons) would provide an access to these fundamental interactions on the atomic scale. Here in order to be able to excite the magnons by means of spin-polarized electrons we couple a Ni monolayer to one and two atomic layers of Co and probe the magnon dispersion relation up to the Brillouin zone boundary. Comparing to the results of ab initio calculations we quantify the complex pattern of the magnetic exchange interaction in the Ni monolayer. We show that, although the magnons in this system are rather stiff, the Heisenberg exchange coupling between the Ni spins is weak. We unravel the origin of the observed large magnon stiffness constant, being a consequence of the small spin density of the Ni atoms.

While the existence of a magnetic field induced quantum spin liquid in Kitaev magnets remains under debate, its topological properties often extend to proximal phases where they can lead to unusual behaviors of both fundamental and applied interests. Subjecting a generic nearest-neighbor spin model of Kitaev magnets to a sufficiently strong in-plane magnetic field, we study the resulting polarized phase and the associated magnon excitations. In contrast to the case of an out-of-plane magnetic field where the magnon band topology is enforced by symmetry, we find that it is possible for topologically trivial and nontrivial parameter regimes to coexist under in-plane magnetic fields. We map out the topological phase diagrams of the magnon bands, revealing a rich pattern of variation of the Chern number over the parameter space and the field angle. We further compute the magnon thermal Hall conductivity as a weighted summation of Berry curvatures, and discuss experimental implications of our results to planar thermal Hall effects in Kitaev magnets.

The entanglement of many localized spins (LSs) within solid magnetic materials is a topic of great basic and applied interest, particularly after becoming amenable to experimental scrutiny where recent neutron scattering experiments have witnessed macroscopic entanglement in the ground state (GS) of antiferromagnets persisting even at elevated temperatures. On the other hand, spintronics and magnonics studies assume that LSs of antiferromagnets are in unentangled Néel GS, as well as that they evolve, when pushed out of equilibrium by current or external fields, according to the Landau-Lifshitz-Gilbert (LLG) equation viewing LSs as classical vectors of fixed length. The prerequisite for applicability of the LLG equation is zero entanglement in the underlying many-body quantum state of LSs. In this study, we initialize quantum Heisenberg ferro- or antiferromagnetic chains hosting $S=1/2, S=1$, or $S=5/2$ LSs into an unentangled pure state and then evolve them by quantum master equations (QMEs) of Lindblad or non-Markovian type, derived by coupling LSs weakly to a bosonic bath (due to phonons in real materials) or by using additional “reaction coordinate” in the latter case. The time evolution is initiated by applying an external magnetic field, and entanglement of the ensuing mixed quantum states is monitored by computing its negativity. We find that non-Markovian dynamics never brings entanglement to zero, in the presence of which the vector of spin expectation value changes its length to render the LLG equation inapplicable. Conversely, Lindbladian (i.e., Markovian) dynamics ensures that entanglement goes to 0, thereby enabling quantum-to-classical transition in all cases—$S=1/2, S=1$, and $S=5/2$ ferromagnets or $S=5/2$ antiferromagnets—except for $S=1/2$ and $S=1$ antiferromagnets. Finally, we investigate the stability of an entangled antiferromagnetic GS upon suddenly coupling it to bosonic baths.