We study high-temperature spin transport through an anisotropic spin-$\frac{1}{2}$ Heisenberg chain in which integrability is broken by a single impurity close to the center of the chain. For a finite impurity strength, the level spacing statistics of this model is known to be Wigner-Dyson. Our aim is to understand if this integrability breaking is manifested in the high-temperature spin transport. We focus first on the nonequilibrium steady state (NESS), where the chain is connected to spin baths that act as sources and sinks for spin excitations at the boundaries. Using a combination of open quantum system theory and matrix product operators techniques, we extract the transport properties by means of a finite-size scaling of the spin current in the NESS. Our results indicate that, despite the formation of a partial domain wall in the steady state magnetization (and despite the Wigner-Dyson level spacing distribution of the model), transport remains ballistic. We contrast this behavior with the one produced by a staggered magnetic field in the XXZ chain, for which it is known that transport is diffusive. By performing a numerical computation of the real part of the spin conductivity, we show that our findings are consistent with linear response theory. We discuss subtleties associated with the apparent vanishing of the Drude in the presence of an impurity.

We consider periodically driven Anderson insulators. The short-time behavior for weak, monochromatic, uniform electric fields is given by linear response theory and was famously derived by Mott. We go beyond this to consider both long times—which is the physics of Floquet late time states—and strong electric fields. This results in a “phase diagram” in the frequency-field strength plane, in which we identify four distinct regimes. These are a linear response regime dominated by preexisting Mott resonances, which exists provided Floquet saturation is not reached within a period; a nonlinear perturbative regime, which exhibits multiphoton-absorption in response to the field; a near-adiabatic regime, which exhibits a primarily reactive response spread over the entire sample and is insensitive to preexisting resonances; and finally an enhanced dissipative regime.

In a quantum Hall system, the finite-wave-vector Hall conductivity displays an intriguing dependence on the Hall viscosity, a coefficient that describes the nondissipative response of the fluid to a velocity gradient. In this paper, we pursue this connection in detail for quantum Hall systems on a lattice, noting that the neat continuum relation breaks down and develops corrections due to the broken rotational symmetry. In the process, we introduce a new, quantum mechanical derivation of the finite-wave-vector Hall conductivity for the integer quantum Hall effect, which allows terms to arbitrary order in the wave-vector expansion to be calculated straightforwardly. We also develop a universal formalism for studying quantum Hall physics on a lattice, and find that at weak applied magnetic fields, generic lattice wave functions connect smoothly to the Landau levels of the continuum. At moderate field strengths, the lattice corrections can be significant and perturb the wave functions, energy levels, and transport properties from their continuum values. Our approach allows the finite-field behavior of a system to be inferred directly from the zero-field band structure.

An efficient technique for calculating x-ray Raman scattering spectra at the $K$ edge in the framework of a single-particle theory is presented. It is based on a recursive method to compute the dynamic structure factor as a continued fraction without requiring the explicit calculation of high-lying unoccupied electronic states. Multipole transitions are calculated to provide a full account of the $q$-dependence of $K$ edges recorded in a series of lithium-bearing reference compounds, namely ${\mathrm{LiBO}}_2$, ${\mathrm{Li}}_2{\mathrm{CO}}_3$, ${\mathrm{Li}}_2\mathrm{O}$, and LiF. The good agreement obtained between experimental and theoretical spectra validates our approach and provides a solid foundation for analyzing $K$ edges beyond the dipole approximation.

We study two models of correlated bond and site disorder on the kagome lattice considering both translationally invariant and completely disordered systems. The models are shown to exhibit a perfectly flat ground-state band in the presence of disorder for which we provide exact analytic solutions. Whereas in one model the flat band remains gapped and touches the dispersive band, the other model has a finite gap, demonstrating that the band touching is not protected by topology alone. Our model also displays fully saturated ferromagnetic ground states in the presence of repulsive interactions, an example of disordered flat band ferromagnetism.

Using spin- and angle-resolved photoemission spectroscopy and relativistic many-body calculations, we investigate the evolution of the electronic structure of ${\left({\mathrm{Bi}}_{1-x}{\mathrm{In}}_x\right)}_2{\mathrm{Se}}_3$ bulk single crystals around the critical point of the trivial to topological insulator quantum-phase transition. By increasing $x$, we observe how a surface gap opens at the Dirac point of the initially gapless topological surface state of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$, leading to the existence of massive fermions. The surface gap monotonically increases for a wide range of $x$ values across the topological and trivial sides of the quantum-phase transition. By means of photon-energy-dependent measurements, we demonstrate that the gapped surface state survives the inversion of the bulk bands which occurs at a critical point near $x=0.055$. The surface state exhibits a nonzero in-plane spin polarization which decays exponentially with increasing $x$, and which persists in both the topological and trivial insulator phases. Our calculations reveal qualitative agreement with the experimental results all across the quantum-phase transition upon the systematic variation of the spin-orbit coupling strength. A non-time-reversal symmetry-breaking mechanism of bulk-mediated scattering processes that increase with decreasing spin-orbit coupling strength is proposed as explanation.

Optomagnonic systems, where light couples coherently to collective excitations in magnetically ordered solids, are currently of high interest due to their potential for quantum information processing platforms at the nanoscale. Efforts so far, both at the experimental and theoretical level, have focused on systems with a homogeneous magnetic background. A unique feature in optomagnonics is, however, the possibility of coupling light to spin excitations on top of magnetic textures. We propose a cavity-optomagnonic system with a nonhomogeneous magnetic ground state, namely, a vortex in a magnetic microdisk. In particular, we study the coupling between optical whispering gallery modes to magnon modes localized at the vortex. We show that the optomagnonic coupling has a rich spatial structure and that it can be tuned by an externally applied magnetic field. Our results predict cooperativities at maximum photon density of the order of $\mathcal{C}\approx {10}^{-2}$ by proper engineering of these structures.

Higher-order topological insulators have a modified bulk-boundary correspondence compared to other topological phases: instead of gapless edge or surface states, they have gapped edges and surfaces, but protected modes at corners or hinges. Here, we explore symmetry-protected topological phases in strongly interacting many-body systems with this generalized bulk-boundary correspondence. We introduce several exactly solvable bosonic lattice models as candidates for interacting higher-order symmetry-protected topological (HOSPT) phases protected by spatial symmetries, and develop a topological field theory that captures the nontrivial nature of the gapless corner and hinge modes. We show how, for rotational symmetry, this field theory leads to a natural relationship between HOSPT phases and conventional SPT phases with an enlarged internal symmetry group. We also explore the connection between bosonic and fermionic HOSPT phases in the presence of strong interactions, and comment on the implications of this connection for the classification of interacting fermionic HOSPT phases. Finally, we explore how gauging internal symmetries of these phases leads to topological orders characterized by nontrivial braiding statistics between topological vortex excitations and geometrical defects related to the spatial symmetry.

Two-particle generalized susceptibilities and their irreducible vertex functions play a prominent role in the quantum many-body theory for correlated electron systems. They act as basic building blocks in the parquet formalism which provides a flexible scheme for the calculation of spectral and response functions. The irreducible vertices themselves have recently attracted increased attention as unexpected divergences in these functions have been identified. Remarkably, such singularities appear already for one of the simplest strongly interacting systems: the atomic limit of the half-filled Hubbard model (Hubbard atom). In this paper, we calculate the analytical expressions for all two-particle irreducible vertex functions of the Hubbard atom in all scattering channels as well as the fully irreducible two-particle vertices. We discuss their divergences and classify them by the eigenvalues and eigenvectors of the corresponding generalized susceptibilities. In order to establish a connection to the recently found multivaluedness of the exact self-energy functional $\mathrm{\Sigma }\left[G\right]$, we show that already an approximation akin to iterated perturbation theory is sufficient to capture, qualitatively, the divergent structure of the vertex functions. Finally, we show that the localized divergences in the disordered binary mixture model are directly linked to a minimum in the single-particle Matsubara Green's function.

In this Rapid Communication we predict several types of topological semimetals that exhibit a bulk quadrupole moment. These semimetals are modeled with a three-dimensional extension of the two-dimensional quadrupole topological insulator. One type of semimetal has bulk nodes and gapped, topological surfaces. A second type, which we may call a higher-order topological semimetal, has a gapped bulk, but harbors a Dirac semimetal with an even number of nodes on one or more surfaces. The final type has a gapped bulk, but harbors half of a Dirac semimetal on multiple surfaces. Each of these semimetals gives rise to midgap hinge states and hinge charge, as well as surface polarization, which are all consequences of a bulk quadrupole moment. We show how the bulk quadrupole moments of these systems can be calculated from the momentum locations of bulk or surface nodes in the energy spectrum. Finally, we illustrate that in some cases it is useful to examine nodes in the Wannier bands, instead of the energy bands, to extract the bulk quadrupole moment.

We employ the weak-coupling renormalization group approach to study unconventional superconducting phases emerging in the extended, repulsive Hubbard model on paradigmatic two-dimensional lattices. Repulsive interactions usually lead to higher-angular momentum Cooper pairing. By considering not only longer-ranged hoppings, but also nonlocal electron-electron interactions, we are able to find superconducting solutions for all irreducible representations on the square and hexagonal lattices, including extended regions of chiral topological superconductivity. For the square, triangular and honeycomb lattices, we provide detailed superconducting phase diagrams as well as the coupling strengths which quantify the corresponding critical temperatures depending on the band-structure parameters, band filling, and interaction parameters. We discuss the sensitivity of the method with respect to the numerical resolution of the integration grid and the patching scheme. Eventually, we show how to efficiently reach a high numerical accuracy.

We present a comprehensive small-angle neutron scattering study of the doping dependence of the helimagnetic correlations in ${\mathrm{Mn}}_{1-x}{\mathrm{Fe}}_x\mathrm{Si}$. The long-range helimagnetic order in ${\mathrm{Mn}}_{1-x}{\mathrm{Fe}}_x\mathrm{Si}$ is suppressed with increasing Fe content and disappears for $x>x^{*}\approx 0.11$, i.e., well before $x_C\approx 0.17$ where the transition temperature vanishes. For $x>x^{*}$, only finite isotropic helimagnetic correlations persist which bear similarities with the magnetic correlations found in the precursor phase of MnSi. Magnetic fields gradually suppress and partly align these short-ranged helimagnetic correlations along their direction through a complex magnetization process.

Topological multipole insulators are a class of higher-order topological insulators (HOTIs) in which robust fractional corner charges appear due to a quantized electric multipole moment of the bulk. This bulk-corner correspondence has been expressed in terms of a topological invariant computed using the eigenstates of the Wilson loop operator, a so-called “nested Wilson loop” procedure. We show that, similar to the unitary Floquet operator describing periodically driven systems, the unitary Wilson loop operator can realize “anomalous” phases that are topologically nontrivial despite having a trivial topological invariant. We introduce a concrete example of an anomalous HOTI, which has a quantized bulk quadrupole moment and fractional corner charges, but a vanishing nested Wilson loop index. An invariant able to capture the topology of this phase is then constructed. Our work shows that anomalous topological phases, previously thought to be unique to periodically driven systems, can occur and be used to understand purely time-independent HOTIs.

By means of scanning tunneling microscopy and spectroscopy, we investigate the electronic properties of lead islands (width 5–100 nm, thickness 5–25 monolayers) deposited by molecular beam epitaxy on twisted graphene layers grown on SiC(000-1). We find that elastic scattering processes govern the local density of states probed at the surface of the Pb islands, inducing (i) the well-known quantum well states due to electron confinement in the direction perpendicular to the surface and (ii) spatial in-plane periodic modulations related to quasiparticle interferences off the island edges. Through a quantitative analysis of these effects, compared with ab initio calculations for a two-dimensional Pb slab, we conclude that the lead islands grown on the surface of graphene can be considered as freestanding from the point of view of their electronic structure, leaving the surrounding graphene layer unperturbed. Accordingly, low bias tunneling spectra show evidence of a sizable interface resistance. Nevertheless, we suggest that the transparency of the interface, which can be estimated from its resistance, is good enough to induce superconductivity within the underlying graphene layer by proximity effect with the Pb islands.

We clarify the physical origin of anomalies in transverse resistivity often observed in exotic materials, such as ${\mathrm{SrRuO}}_3$, in which the Berry curvature is manifested in the transport properties. The previously attributed mechanism for the anomalies, the topological Hall effect (THE) [e.g., J. Matsuno et al., Sci. Adv. 2, e160030 (2016)], is refuted by our thorough investigations as well as formulation of a model considering inhomogeneous magnetoelectric properties in the material. Our analyses fully explain every feature of the anomalies without resorting to the THE. The present results establish a fundamental understanding, which was previously overlooked, of magnetotransport properties in such exotic materials.

Two-dimensional transition-metal dichalcogenides $M{X}_2({\mathrm{MoS}}_2,{\mathrm{WS}}_2,{\mathrm{MoSe}}_2$,...) are among the most promising materials for band-gap engineering. Widely studied in these compounds, by means of ab initio techniques, is the possibility of tuning the direct-indirect gap character by means of in-plane strain. In such kind of calculations however the lattice degrees of freedom are assumed to be classical and frozen. In this paper we investigate in details the dependence of the band-gap character (direct vs indirect) on the out-of-plane distance $h$ between the two chalcogen planes in each $M{X}_2$ unit. Using DFT calculations, we show that the band-gap character is indeed highly sensitive on the parameter $h$, in monolayer as well as in bilayer and bulk compounds, permitting for instance the switching from indirect to direct gap and from indirect to direct gap in monolayer systems. This scenario is furthermore analyzed in the presence of quantum lattice fluctuation induced by the zero-point motion. On the basis of a quantum analysis, we argue that the direct-indirect band-gap transitions induced by the out-of-plane strain as well as by the in-plane strain can be regarded more as continuous crossovers rather than as real sharp transitions. The consequences on the physical observables are discussed.

Using photoelectron diffraction and spectroscopy, we explore the structural and electronic properties of the hexagonal boron nitride $(h$-BN) monolayer epitaxially grown on the Co(0001) surface. Perfect matching of the lattice parameters allows formation of a well-defined interface where the B atoms occupy the hollow sites while the N atoms are located above the Co atoms. The corrugation of the $h$-BN monolayer and its distance from the substrate were determined by means of R-factor analysis. The obtained results are in perfect agreement with the density functional theory (DFT) predictions. The electronic structure of the interface is characterized by a significant mixing of the $h$-BN and Co states. Such hybridized states appear in the $h$-BN band gap. This allows to obtain atomically resolved scanning tunneling microscopy (STM) images from the formally insulating 2D material being in contact with ferromagnetic metal. The STM images reveal mainly the nitrogen sublattice due to a dominating contribution of nitrogen orbitals to the electronic states at the Fermi level. We believe that the high quality, well-defined structure and interesting electronic properties make the $h$-BN/Co(0001) interface suitable for spintronic applications.

The infinite time-evolving block decimation algorithm is applied to calculate the dynamical spin-structure factors of the quasi-one-dimensional (Q1D) $S=1$ antiferromagnetic spin system with single-ion anisotropy and bond alternation. It is found that when the staggered field induced by the weak interchain interaction is taken into account, the excitation continuum originating from magnons is quantized. The excitation energies of the quantized excitation spectra are well explained by the negative zeros of the Airy functions, when the single-ion anisotropy is negatively strong. This quantization of the magnon continuum is a counterpart of the spinon confinement, which has been recently discussed for Q1D $S=1/2$ antiferromagnets. It is further shown that, when a staggered field exists, the quantized excitation spectra appear on the phase boundary between the Haldane and Néel phases of the phase diagram without the staggered field. However, the quantized excitation spectra disappear in the singlet-dimer phase.

The study of exotic one-dimensional states, particularly those at the edges of topological materials, demand new experimental probes that can access the interplay between charge and spin degrees of freedom. One potential approach is to use a single spin probe, such as a nitrogen vacancy center in diamond, which has recently emerged as a versatile tool to probe nanoscale systems in a noninvasive fashion. Here, we present a theory describing how noise magnetometry with spin probes can directly address several questions that have emerged in experimental studies of 1D systems, including those in topological materials. We show that by controlling the spin degree of freedom of the probe, it is possible to measure locally and independently local charge and spin correlations of 1D systems. Visualization of 1D edge states, as well as sampling correlations with wave-vector resolution can be achieved by tuning the probe-to-sample distance. Furthermore, temperature-dependent measurements of magnetic noise can clearly delineate the dominant scattering mechanism (impurities versus interactions)—this is of particular relevance to quantum spin Hall measurements where conductance quantization is not perfect. The possibility to probe both charge and spin excitations in a wide range of length scales opens new pathways to bridging the large gap between atomic scale resolution of scanning probes and global transport measurements.

We study noise-averaged observables for a system of exchange-coupled quantum spins (qubits), each subject to a stochastic drive, by establishing mappings onto stochastic models in the strong-noise limit. Averaging over noise yields Lindbladian equations of motion; when these are subjected to a strong-noise perturbative treatment, classical master equations are found to emerge. The dynamics of noise averages of operators displays diffusive behavior or exponential relaxation, depending on whether the drive conserves one of the spin components or not. In the latter case, the second moment of operators, from which the average subsystem purity and out-of-time-order correlation functions can be extracted, is described by the Fredrickson-Andersen model, originally introduced as a model of cooperative relaxation near the glass transition. It is known that fluctuations of a ballistically propagating front in the model are asymptotically Gaussian in one dimension. We extend this by conjecturing, with strong numerical evidence, that in two dimensions the long-time fluctuations are in the Kardar-Parisi-Zhang universality class, complementing a similar observation in random unitary circuits.