Higher-order topological (HOT) phases feature boundary (such as corner and hinge) modes of codimension $d_c>1$. We here identify an antiunitary operator that ensures the spectral symmetry of a two-dimensional HOT insulator and the existence of cornered localized states ($d_c=2$) at precise zero energy. Such an antiunitary symmetry allows us to construct a generalized HOT insulator that continues to host corner modes even in the presence of a weak anomalous Hall insulator and spin-orbital density-wave orderings, and is characterized by a quantized quadrupolar moment $Q_{xy}=0.5$. Similar conclusions can be drawn for the time-reversal symmetry breaking HOT $p+id$ superconductor and the corner localized Majorana zero modes survive even in the presence of weak Zeeman coupling and $s$-wave pairing. Such HOT insulators also serve as the building blocks of three-dimensional second-order Weyl semimetals, supporting one-dimensional hinge modes.

In topological mechanics, the identification of a mechanical system's rigidity matrix with an electronic tight-binding model allows one to infer topological properties of the mechanical system, such as the occurrence of “floppy” boundary modes, from the associated electronic band structure. Here, we introduce an approach to systematically construct topological mechanical systems by an exact supersymmetry (SUSY) that relates the bosonic (mechanical) and fermionic (e.g., electronic) degrees of freedom. As examples we discuss mechanical analogs of the Kitaev honeycomb model and of a second-order topological insulator with floppy corner modes. Our SUSY construction naturally defines a set of topological invariants for bosonic (mechanical) systems, such as bosonic Wilson loop operators that are formulated in terms of a SUSY-related fermionic Berry curvature.

The recently discovered superconductivity in ${\mathrm{Nd}}_{1-x}{\mathrm{Sr}}_x{\mathrm{NiO}}_2$ provides a new opportunity for studying strongly correlated unconventional superconductivity. The single-hole ${\mathrm{Ni}}^{+}$ $\left(3d^9\right)$ configuration in the parent compound ${\mathrm{NdNiO}}_2$ is similar to that of ${\mathrm{Cu}}^{2+}$ in cuprates. We suggest that after doping, the intraorbital spin-singlet and interorbital spin-triplet double-hole (doublon) configurations of ${\mathrm{Ni}}^{2+}$ are competing, and we construct a two-band Hubbard model by including both the $3d_{x^2-y^2}$ and $3d_{xy}$ orbitals. The effective spin-orbital superexchange model in the undoped case is a variant of the $\text{SU}\left(4\right)$ Kugel-Khomskii model augmented by symmetry-breaking terms. Upon doping, the effective exchange interactions between spin-$\frac{1}{2}$ single holes, spin-1 (triplet) doublons, and singlet doublons are derived. Possible superconducting pairing symmetries are classified in accordance to the $D_{4h}$ crystalline symmetry, and their connections to the superexchange interactions are analyzed.

Higher-order topological (HOT) states, hosting topologically protected modes on lower-dimensional boundaries, such as hinges and corners, have recently extended the realm of the static topological phases. Here we demonstrate the possibility of realizing a two-dimensional Floquet second-order topological insulator, featuring corner-localized zero quasienergy modes and characterized by quantized Floquet qudrupolar moment $Q_{xy}^{\mathrm{Flq}}=0.5$, by periodically kicking a quantum spin Hall insulator (QSHI) with a discrete fourfold ($C_4$) and time-reversal ($\mathcal{T}$) symmetry breaking Dirac mass perturbation. Furthermore, we show that $Q_{xy}^{\mathrm{Flq}}$ becomes independent of the choice of origin as the system approaches the thermodynamic limit. We also analyze the dynamics of a corner mode after a sudden quench, when the $C_4$ and $\mathcal{T}$ symmetry breaking perturbation is switched off, and find that the corresponding survival probability displays periodic appearances of complete, partial and no revival for long time, encoding the signature of corner modes in a QSHI. Our protocol is sufficiently general to explore the territory of dynamical HOT phases in insulators and gapless systems.

We consider a general problem of a Josephson contact between two multiband superconductors with coexisting superconducting and magnetic phases. As a particular example, we use the quasiclassical theory of superconductivity to study the properties of a Josephson contact between two disordered $s^{\pm }$-wave superconductors allowing for the coexistence between superconductivity and spin-density-wave orders. The intra- and interband disorder-induced scattering is treated within the self-consistent Born approximation. We calculate the spatial profile of the corresponding order parameters on both sides of the interface with a finite reflection coefficient and use our results to evaluate the local density of states at the interface as well as critical supercurrent through the junction as a function of phase or applied voltage. Our methods are particularly well suited for describing spatially inhomogeneous states of iron-based superconductors where controlled structural disorder can be created by an electron irradiation. We reveal the connection between our theory and the circuit theory of Andreev reflection and extend it to superconducting junctions of arbitrary nature. Lastly, we outline directions for further developments in the context of proximity circuits of correlated electron systems.

Majorana fermions are predicted to arise at the ends of nanowire devices which combine superconductivity, strong spin-orbit coupling, and an external magnetic field. By manipulating networks of these devices with suitable gating, it has been suggested that braiding operations may be performed which act as logic operations, suitable for quantum computation. However, the unavoidable misalignment of the magnetic field in any realistic device geometry has raised questions about the feasibility of such braiding. In this paper, we numerically simulate braiding operations in devices with Y-junction and tuning-fork geometries using an experimentally motivated nanowire model. We study how the static and dynamical features vary with geometric parameters and identify parameter choices that optimize the probability of a successful braid. Notably, we find that there is an optimal Y-junction half-angle (about ${20}^{\circ }$ for our parameter values), which balances two competing mechanisms that reduce the energy gap to excitations. In addition, we find that a tuning-fork geometry has significant advantages over a Y-junction geometry, as it substantially reduces the effect of dynamical phase oscillations that complicate the braiding process. Our results suggest that performing a successful braid is in principle possible with such devices and is within experimental reach.

We study the effect of electron interaction in an electronic system with a high-order Van Hove singularity, where the density of states shows a power-law divergence. Owing to scale invariance, we perform a renormalization group (RG) analysis to find a nontrivial metallic behavior where various divergent susceptibilities coexist but no long-range order appears. We term such a metallic state as a supermetal. Our RG analysis reveals noninteracting and interacting fixed points, which draws an analogy to the ${\varphi }^4$ theory. We further present a finite anomalous dimension at the interacting fixed point by a controlled RG analysis, thus establishing an interacting supermetal as a non-Fermi liquid.

The topological features of quantum many-body wave functions are known to have profound consequences for the physics of ground-states and their low-energy excitations. We describe how topology influences the dynamics of many-body systems when driven far from equilibrium. Our results are succinctly captured by a nonequilibrium topological classification that can be used to predict universal aspects of generic isolated quantum systems as they evolve unitarily in time. By analogy to the classifications used to describe systems in equilibrium, we consider two short-ranged entangled wave functions to be topologically equivalent if they can be interconverted via finite-time unitary evolution governed by a symmetry-respecting Hamiltonian. We demonstrate that this definition captures the salient features of these systems in a broad range of nonequilibrium scenarios. As well as providing conceptual insights into the constraints imposed by topology on many-body dynamics, we discuss the practical implications of our findings. In particular, we show that the characteristic zero-frequency spectroscopic peaks associated with topologically protected edge modes will be broadened by external noise only when the system is trivial in the nonequilibrium classification.

As they do not rely on the presence of any crystal symmetry, Weyl nodes are robust topological features of an electronic structure that can occur at any momentum and energy. Acting as sinks and sources of Berry curvature, Weyl nodes have been predicted to strongly affect the transverse electronic response, like in the anomalous Hall or Nernst effects. However, to observe large anomalous effects the Weyl nodes need to be close to or at the Fermi level, which implies the band structure must be tuned by an external parameter, e.g., chemical doping. Here we show that in a ferromagnetic metal tuning of the Weyl node energy and momentum can be achieved by rotation of the magnetization. First, taking as example the elementary magnet hcp-Co, we use electronic structure calculations based on density-functional theory to show that by canting the magnetization away from the easy axis, Weyl nodes can be driven exactly to the Fermi surface. Second, we show that the same phenomenology applies to the kagome ferromagnet ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$, in which we additionally show how the dynamics in energy and momentum of the Weyl nodes affects the calculated anomalous Hall and Nernst conductivities. Our results highlight how the intrinsic magnetic anisotropy can be used to engineer Weyl physics.

We study vortex motion using a Hopf flow on a 3-sphere, in place of the standard 3-torus defined by periodic boundary conditions. Although both of these underlying manifolds look locally like ${\mathbb{R}}^3$, the vortex behavior differs significantly. This raises the question of how well calculations on the 3-torus correspond to behavior in ${\mathbb{R}}^3$, for this problem or others. We find that, on both the 3-sphere and 3-torus, vortex tangles appear, with their line density related to the strength of the driving velocity field. However, tangles on the 3-sphere are highly anisotropic, with vortices tending to align along the flow direction. Standard power-law dependences change accordingly from their values in more isotropic tangles. The line length density $\langle L\rangle$ is proportional to $v_{ns}^{1.28}$, where $v_{ns}$ is the drive velocity, and the reconnection rate depends roughly on ${\langle L\rangle }^2$. These compare to $v_{ns}^2$ and ${\langle L\rangle }^{2.5}$ for the more isotropic tangles on the 3-torus. In addition, in simulations using the local induction approximation rather than the full Biot-Savart law, the tangle collapses so that all vortices are nearly aligned with a single flow line. By contrast, vortices on the 3-torus become perpendicular to the driving velocity.

Macroscale continuum mechanics simulations rely on material properties stemming from the microscale, which are normally described using predetermined phenomenological equations of state (EOS), which depend on physical parameters usually obtained from experiments. A method is proposed for the automatic generation of first-principles unconstrained EOSs using a Gaussian process on a set of ab initio molecular dynamics simulations, thereby closing the continuum equations with the accuracy determined by the underlying first-principles theory. The method is validated for bulk silicon using density-functional theory (DFT) by comparing planar (one-dimensional) shock waves with experiment, and also with an explicit first-principles molecular dynamics simulation, both in the hyperelastic regime. Its applicability is then illustrated it for two-dimensional shock waves in DFT bulk silicon, following their nonlinear, temperature-dependent, anisotropic dynamics after a cylindrical region is instantaneously heated. The method is applicable to condensed matter systems in other regimes, using well-known continuum techniques and/or molecular dynamics simulations at larger scales.

Topological properties of physical systems have attracted tremendous interest in condensed matter and atomic physics in the last decade. Recently, magnetic solid state compounds with and without magnetic order have become a focus. We provide evidence that ${\mathrm{BiCu}}_2{\mathrm{PO}}_6$ is a gapful, disordered quantum antiferromagnet with a non-trivial finite Zak phase, which characterizes one-dimensional systems. Our calculations show that in spite of the non-trivial topology no localized edge modes occur. This unexpected behavior is explained by a generic feature, namely the significance of direct and indirect gaps in topological systems.

Spin inertia measurements are a novel experimental tool to study long-time spin relaxation processes in semiconductor nanostructures. We develop a theory of the spin inertia effect for resident electrons and holes localized in quantum dots. We consider the spin orientation by short optical pulses with arbitrary pulse area and detuning from the trion resonance. The interaction with an external longitudinal magnetic field and the hyperfine interaction with the nuclear spin bath is considered in both the ground and excited (trion) states of the quantum dots. We analyze how the spin inertia signal depends on the magnetic field (polarization recovery) and on the modulation frequency of the helicity of the pump pulses as well as on their power and detuning. In particular, we elaborate how approaching the saturation limit of the spin polarization influences the measurements. The quantitative description of spin inertia measurements will enable the determination of the parameters of spin dynamics such as the spin relaxation times in the ground and excited states and the parameters of the hyperfine interaction. Finally, we predict the emergence of resonant spin amplification due to the transverse components of the nuclear spin fluctuations, which manifests itself as oscillations of the spin polarization as a function of the longitudinal magnetic field.

Simulations of quantum transport in coherent conductors have evolved into mature techniques that are used in fields of physics ranging from electrical engineering to quantum nanoelectronics and material science. The most efficient general-purpose algorithms have a computational cost that scales as $L^{6,\cdots ,7}$ in three dimensions ($L$: length of the device), which on the one hand is a substantial improvement over older algorithms, but on the other hand still severely restricts the size of the simulation domain, limiting the usefulness of simulations through strong finite-size effects. Here we present a class of algorithms that, for certain systems, allows us to directly access the thermodynamic limit. Our approach, based on the Green's function formalism for discrete models, targets systems that are mostly invariant by translation, i.e., invariant by translation up to a finite number of orbitals and/or quasi-one-dimensional electrodes and/or the presence of edges or surfaces. Our approach is based on an automatic calculation of the poles and residues of series expansions of the Green's function in momentum space. This expansion allows us to integrate analytically in one momentum variable. We illustrate our algorithms with several applications: devices with graphene electrodes that consist of half an infinite sheet, Friedel oscillation calculations of infinite two-dimensional systems in the presence of an impurity, quantum spin Hall physics in the presence of an edge, and the surface of a Weyl semimetal in the presence of impurities and electrodes connected to the surface. In this last example, we study the conduction through the Fermi arcs of the topological material and its resilience to the presence of disorder. Our approach provides a practical route for simulating three-dimensional bulk systems or surfaces as well as other setups that have so far remained elusive.

We address the problem of electronic and nuclear spin resonance of an individual atom on a surface driven by a scanning tunneling microscope. Several mechanisms have been proposed so far, some of them based on the modulation of exchange and crystal field associated with a piezoelectric displacement of the adatom driven by the radio frequency (RF) tip electric field. Here we consider another mechanism, where the piezoelectric displacement modulates the $g$-factor anisotropy, leading both to electronic and nuclear spin flip transitions. We discuss thoroughly the cases of hydrogenated Ti ($S=1/2$) and Fe $(S=2)$ on MgO, relevant for recent experiments. We model the system using two approaches. First, an analytical model that includes crystal field, spin orbit coupling, and hyperfine interactions. Second, we carry out density-functional-based calculations. We find that the modulation of the anisotropy of the $g$ tensor due to the piezoelectric displacement of the atom is an additional mechanism for scanning tunneling microscopy (STM)-based single spin resonance that would be effective in $S=1/2$ adatoms with large spin orbit coupling. In the case of hydrogenated Ti on MgO, we predict a modulation spin resonance frequency driven by the DC electric field of the tip.

We investigate low-temperature electronic states of the series of organic conductors ${\beta }^{\prime \prime }-{\left[\text{bis(ethylenedithio)tetrathiafulvalene}\right]}_4\left[\left({\mathrm{H}}_3\mathrm{O}\right)M{\left({\mathrm{C}}_2{\mathrm{O}}_4\right)}_3\right]G$, where $M$ and $G$ represent trivalent metal ions and guest organic molecules, respectively. Our structural analyses reveal that the replacement of $M$ and $G$ give rise to systematic change in the cell parameters, especially in the $b$-axis length, which has a positive correlation with the superconducting transition temperature $T_{\mathrm{c}}$. Analysis of temperature and magnetic field dependences of the electrical resistance including the Shubnikov–de Haas oscillations elucidates that the variation of charge disproportionation, the effective mass, and the number of itinerant carriers can be systematically explained by the change of the $b$-axis length. The changes of the transfer integrals induced by stretching/compressing the $b$ axis are confirmed by the band calculation. We discuss that electron correlations in quarter-filled electronic bands lead to charge disproportionation and the possibility of a novel pairing mechanism of superconductivity mediated by charge degrees of freedom.

One of the main difficulties of observing many-body localization in natural solid-state materials is creating strong enough disorder. A strong random local magnetic field is difficult to achieve in a solid state material. We propose exploiting large random magnetic anisotropy, either in magnitude or direction, which can be realized in organometallic quantum magnets. We present the phase diagram of an $S=1$ Heisenberg chain in terms of both a random magnetic anisotropy and a random magnetic field. The many-body localization phase emerges with sufficiently large anisotropy under very small random fields. We propose candidate materials of doped single-chain organometallic quantum magnets for realizing many-body localization, where either orientation disorder or substitution of metal ions can create large random magnetic anisotropy required in our prediction.

We study the effects of temperature on the topological nature of ${\mathrm{ZrTe}}_5$, which sits near the phase boundary between strong and weak topological insulating orders. Using first-principles calculations, we show that the band gap and the topological indices of ${\mathrm{ZrTe}}_5$ are extremely sensitive to thermal expansion and that the electron-phonon interaction accounts for more than a third of the total temperature-dependent effects in ${\mathrm{ZrTe}}_5$. We find that the temperature dependence of the band gap has an opposite sign in the strong and weak topological insulator phases. Based on this insight, we propose a robust and unambiguous method to determine the topological nature of any given sample of ${\mathrm{ZrTe}}_5$: If the band gap decreases with temperature it is a strong topological insulator, and if it increases with temperature it is a weak topological insulator. An analogous strategy is expected to be generally applicable to other materials and to become particularly important in the vicinity of topological phase boundaries where other methods provide ambiguous results.

We show that a strained wire of a Weyl semimetal supports another type of gapless excitation, the chiral sound wave (CSW). It is a longitudinal charge density wave analog to the chiral magnetic wave predicted in the quark-gluon plasma but driven by an elastic axial pseudomagnetic field. It involves the axial-axial-axial contribution to the chiral anomaly which couples the chiral charge density to the elastic axial gauge field. The chiral sound is unidirectional: It propagates along the elastic magnetic field and not in the opposite direction. The CSW may propagate for long distances as it does not couple directly to quickly dissipating electromagnetic plasmons, while its damping is controlled by the slow chirality flip rate. We propose an experimental setup to directly detect the chiral sound, which is excited by mechanical vibrations of the crystal lattice in the GHz frequency range. Our findings contribute to the trend, the chiral acoustics, in strained Weyl semimetals.

The many-body localization transition in quasiperiodic systems has been extensively studied in recent ultracold atom experiments. At intermediate quasiperiodic potential strength, a surprising Griffiths-like regime with slow dynamics appears in the absence of random disorder and mobility edges. In this Rapid Communication, we study the interacting Aubry-Andre model, a prototype quasiperiodic system, as a function of incommensurate potential strength using a dynamical measure, information scrambling, in a large system of 200 lattice sites. Between the thermal phase and the many-body localized phase, we find an intermediate dynamical phase where the butterfly velocity is zero and information spreads in space as a power law in time. This is in contrast to the ballistic spreading in the thermal phase and logarithmic spreading in the localized phase. We further investigate the entanglement structure of the many-body eigenstates in the intermediate phase and find strong fluctuations in eigenstate entanglement entropy within a given energy window, which is inconsistent with the eigenstate thermalization hypothesis. Machine learning on the entanglement spectrum also reaches the same conclusion. Our large-scale simulations suggest that the intermediate phase with a vanishing butterfly velocity could be responsible for the slow dynamics seen in recent experiments.