We present a method to compute the intrinsic spin Hall conductivity from first principles using an interpolation scheme based on maximally localized Wannier functions. After obtaining the relevant matrix elements among the ab initio Bloch states calculated on a coarse $k$-point mesh, we Fourier transform them to find the corresponding matrix elements between Wannier states. We then perform an inverse Fourier transform to interpolate the velocity and spin-current matrix elements onto a dense $k$-point mesh and use them to evaluate the spin Hall conductivity as a Brillouin-zone integral. This strategy has a much lower computational cost than a direct ab initio calculation without sacrificing the accuracy. We demonstrate that the spin Hall conductivities of platinum and doped gallium arsenide, computed with our interpolation scheme as a function of the Fermi energy, are in good agreement with those obtained in previous first-principles studies. We also discuss certain approximations that can be performed, in the spirit of the tight-binding method, to simplify the calculation of the velocity and spin-current matrix elements in the Wannier representation.

We consider the Hall conductivity of composite fermions in the theory of Halperin, Lee, and Read (HLR) [B. I. Halperin, P. A. Lee, and N. Read, Phys. Rev. B 47, 7312 (1993)]. We present a fully quantum-mechanical numerical calculation that shows, under suitable conditions, the HLR theory exhibits a particle-hole symmetric dc electrical Hall response in the presence of quenched disorder. Remarkably, this response of the HLR theory remains robust even when the disorder range is of the order of the Fermi wavelength. We find that deviations from the particle-hole symmetric response can appear in the ac Hall conductivity at frequencies sufficiently large compared to the inverse system size. Our results agree with a recent semiclassical analysis by Wang et al. [C. Wang, N. R. Cooper, B. I. Halperin, and A. Stern, Phys. Rev. X 7, 031029 (2017)] and complement the arguments based on the fully quantum-mechanical model by Kumar et al. [P. Kumar, M. Mulligan, and S. Raghu, Phys. Rev. B 98, 115105 (2018)]. These results provide further evidence that the HLR theory is compatible with an emergent particle-hole symmetry.

The fact that the computational cost of simulating a many-body quantum system on a computer increases with the amount of entanglement has been considered as the major bottleneck for simulating its out-of-equilibrium dynamics. Some aspects of the dynamics are, nevertheless, robust under appropriately devised approximations. Here we present a possible algorithm that allows to systematically approximate the equilibration value of local operators after a quantum quench. At the core of our proposal, there is the idea to transform entanglement between distant parts of the system into mixture, and at the same time preserving the local reduced density matrices of the system. We benchmark the resulting algorithm by studying quenches of quadratic fermionic Hamiltonians.

We studied the effect of external pressure on the electrodynamic properties of $\alpha -{\mathrm{Li}}_2{\mathrm{IrO}}_3$ single crystals in the frequency range of the phonon modes and the Ir $d-d$ transitions. The abrupt hardening of several phonon modes under pressure supports the onset of the dimerized phase at the critical pressure $P_c=3.8\mathrm{GPa}$. With increasing pressure an overall decrease in spectral weight of the Ir $d-d$ transitions is found up to $P_c$. Above $P_c$, the local (on-site) $d-d$ excitations gain spectral weight with increasing pressure, which hints at a pressure-induced increase in the octahedral distortions. The nonlocal (intersite) Ir $d-d$ transitions show a monotonic blueshift and decrease in spectral weight. The changes observed for the nonlocal excitations are most prominent well above $P_c$, namely, for pressures $\ge 12$ GPa, and only small changes occur for pressures close to $P_c$. The profile of the optical conductivity at high pressures ($\sim 20$ GPa) appears to be indicative of the dimerized state in iridates.

Topological semimetals with different types of band crossings provide a rich platform to realize novel fermionic excitations, known as topological fermions. In particular, some fermionic excitations can be direct analogs of elementary particles in quantum field theory when both obey the same laws of physics in the low-energy limit. Examples include Dirac and Weyl fermions, whose solid-state realizations have provided new insights into long-sought phenomena in high-energy physics. Recently, theorists predicted new types of fermionic excitations in condensed-matter systems without any high-energy counterpart, and their existence is protected by crystalline symmetries. By studying the topology of the electronic structure in PdBiSe using density functional theory calculations and bulk-sensitive soft x-ray angle-resolved photoemission spectroscopy, we demonstrate a coexistence of four different types of topological fermions: Weyl, Rarita-Schwinger-Weyl, double class-II three-component, and charge-2 fourfold fermions. Our discovery provides a remarkable platform to realize multiple fermions in a single solid, charting the way forward to studies of their potentially exotic properties as well as their interplay.

We considered the question of applying the multiscale entanglement renormalization ansatz (MERA) to describe chiral topological phases. We defined a functional for each layer in the MERA, which captures the correlation length. With some algebraic geometry tools, we rigorously proved its monotonicity with respect to adjacent layers, and the existence of a lower bound for chiral states, which shows a trade-off between the bond dimension and the correlation length. Using this theorem, we showed the number of orbitals per cell (which roughly corresponds to the bond dimension) should grow with the height. Conversely, if we restrict the bond dimensions to be constant, then there is an upper bound of the height. Specifically, we established a no-go theorem stating that we will not approach a renormalization fixed point in this case.

The transversal magnetoresistance associated with the semimetal ${\mathrm{TaAs}}_2$ shows a parabolic field dependence that rises unrestrictedly to 2800 at 14 T and 1.8 K. Here, we report the results of a comprehensive quantum-oscillation study. Angular-dependent de Haas–van Alphen (dHvA) data were obtained with the method of cantilever-torque magnetometry. These were compared with the results of density-functional theory calculations, which predict a Fermi surface with two kinds of electron pockets, as well as two types of hole pockets. Only the electron pockets could be experimentally verified, whereas no evidence for the hole pockets is present in the measured dHvA frequencies.

Understanding strongly correlated systems driven out of equilibrium is a challenging task necessitating the simultaneous treatment of quantum mechanics, dynamical constraints, and strong interactions. A Mott insulator subjected to a uniform and static electric field is prototypical, raising key questions such as the fate of Bloch oscillations with increasing correlation strength, the approach to a steady-state DC transport regime and the role of dissipation in it, and electric-field-driven phase transitions. Despite tremendous efforts over the past decade employing various numerical and analytical approaches, the manner in which a nonequilibrium steady state gets established has remained an unresolved problem. We develop here an effective large-$\mathcal{N}$ Keldysh field theory for studying nonequilibrium transport in a regular one-dimensional dissipative Mott insulator system subjected to a uniform electric field. Upon abruptly turning on the electric field (a quench), a transient oscillatory current response reminiscent of Bloch oscillations is found. In the regime of small tunneling conductance the amplitude of these oscillations, over a large time window, decreases as an inverse square power law in time, ultimately going over to an exponential decay beyond a large characteristic time ${\tau }_d$ that increases with $\mathcal{N}.$ Such a relaxation to a steady-state DC response is absent in the dissipation-free Hubbard chain at half filling. The steady-state current at small fields is governed by large-distance cotunneling, a process absent in the equilibrium counterpart. The low-field DC current has a Landau-Zener-Schwinger form but qualitatively differs from the expression for pair-production probability for the dissipation-free counterpart. The breakdown of perturbation theory in the Mott phase possibly signals a nonequilibrium phase transition to a metallic phase. Our study sheds light on the approach of a driven, dissipative strongly correlated system to a nonequilibrium steady state and also provides a general analytic microscopic framework for understanding other nonequilibrium phenomena in these systems.

The fundamental properties of recently synthesized single- and bilayer ${\mathrm{PdSe}}_2$ are investigated using accurate many-body perturbation GW theory to quantitatively examine their electronic structure and explain the insufficiency of previously reported experimental and theoretical results. Including electron-hole interactions responsible for exciton formation, we solve the Bethe-Salpeter equation on top of the ${\mathrm{GW}}_0$ approximation to predict the optical properties. The fundamental quasiparticle band gaps of single- and bilayer ${\mathrm{PdSe}}_2$ are 2.55 and 1.89 eV, respectively. The optical gap of monolayer ${\mathrm{PdSe}}_2$ reduces significantly due to a large excitonic binding energy of 0.65 eV comparable to that of ${\mathrm{MoSe}}_2$, while an increase of the layer number decreases the excitonic binding energy to 0.25 eV in bilayer ${\mathrm{PdSe}}_2$. The giant band gap renormalization of ∼36–38% in the bilayer (BL) ${\mathrm{PdSe}}_2$/graphene heterostructure has a high impact on the construction of ${\mathrm{PdSe}}_2$-based devices and explains the experimentally observed band gap. The small value of the experimental optical gap of single-layer (SL) ${\mathrm{PdSe}}_2$ (1.3 eV) can be explained by the presence of Se vacancies, which can drop the Tauc-estimated optical gap to ∼1.32 eV. The absorption spectra of both mono- and bilayer ${\mathrm{PdSe}}_2$ cover a wide region of photon energy, demonstrating promising application in solar cells and detectors. These findings provide a basis for a deeper understanding of the physical properties of ${\mathrm{PdSe}}_2$ and ${\mathrm{PdSe}}_2$-based heterostructures.

The problem of the nonlinear spin-currents generated by an electric field $\mathbf{E}$ and a temperature gradient $\mathbf{\nabla }T$ in spin-orbit coupled systems is revisited in a different formalism. Here, the second-order correction to the particle distribution function $\delta f^{\left(2\right)}$ is derived in a semiclassical approximation that takes into account the local change in the equilibrium distribution function induced by the external fields. Our approach departs significantly from the present theory, where $\delta f^{\left(2\right)}$ is written as an iterative solution to the Boltzmann transport equation in the relaxation-time approximation. As we show, such an expression does not actually satisfy the collision term of the equation, and therefore it is not self-consistent. We apply our formalism to the case of a quantum well with arbitrary values of the linear Rashba $\alpha$ and Dresselhaus $\beta$ interactions. For the whole range of $\alpha$ versus $\beta$ values, we obtain analytic results for all the spin currents that can be driven in the system, proportional with ${\mathbf{E}}^2$, $\mathbf{\nabla }{T}^2$, or with $\mathbf{E}·\mathbf{\nabla }T$. The magnitude of these currents is smaller than previously anticipated.

Temperature-dependent magnetic properties of ${\mathrm{Nd}}_2{\mathrm{Fe}}_{14}\mathrm{B}$ permanent magnets, i.e., saturation magnetization $M_{\text{s}}\left(T\right)$, effective magnetic anisotropy constants $K_i^{\text{eff}}\left(T\right)\left(i=1,2,3\right)$, domain-wall width ${\delta }_w\left(T\right)$, and exchange stiffness constant $A_{\text{e}}\left(T\right)$, are calculated by using ab initio informed atomistic spin model simulations. We construct the atomistic spin model Hamiltonian for ${\mathrm{Nd}}_2{\mathrm{Fe}}_{14}\mathrm{B}$ by using the Heisenberg exchange of $\mathrm{Fe}-\mathrm{Fe}$ and $\mathrm{Fe}-\mathrm{Nd}$ atomic pairs, the uniaxial single-ion anisotropy of Fe atoms, and the crystal-field energy of Nd ions, which is approximately expanded into an energy formula featured by second-, fourth-, and sixth-order phenomenological anisotropy constants. After applying a temperature rescaling strategy, we show that the calculated Curie temperature, spin-reorientation phenomenon, $M_{\text{s}}\left(T\right),{\delta }_w\left(T\right)$, and $K_i^{\text{eff}}\left(T\right)$, agree well with the experimental results. $A_{\text{e}}\left(T\right)$ is estimated through a general continuum description of the domain-wall profile by mapping atomistic magnetic moments to the macroscopic magnetization. $A_{\text{e}}$ is found to decrease more slowly than $K_1^{\text{eff}}$ with increasing temperature and approximately scale with normalized magnetization as $A_{\text{e}}\left(T\right)\sim m^{1.2}$. Specifically, the possible domain-wall configurations at temperatures below the spin-reorientation temperature and the associated ${\delta }_w$ and $A_{\text{e}}$ are identified. This work provokes a scale bridge between ab initio calculations and temperature-dependent micromagnetic simulations of Nd-Fe-B permanent magnets.

We demonstrate that the hybrid structures consisting of a superconducting layer with an adjacent spin-textured ferromagnet demonstrate the variety of equilibrium magnetoelectric effects originating from coupling between the conduction electron spin and superconducting current. By deriving and solving the generalized Usadel equation, which takes into account the spin-filtering effect, we find that a supercurrent generates spin polarization in the superconducting film which is noncoplanar with the local ferromagnetic moment. The inverse magnetoelectric effect in such structures is shown to result in the spontaneous phase difference across the magnetic topological defects such as a domain wall and helical spin texture. The possibilities to obtain dissipationless spin torques and detect domain-wall motion through the superconducting phase difference are discussed.

Recent experimental observations of Weyl fermions in materials open a new frontier of condensed-matter physics. Based on first-principles calculations, we here discover the Weyl fermions in a two-dimensional (2D) layered electride material ${\mathrm{Y}}_2\mathrm{C}$. We find that the Y $4d$ orbitals and the anionic $s$-like orbital confined in the interstitial spaces between ${\left[{\mathrm{Y}}_2\mathrm{C}\right]}^{2+}$ cationic layers are hybridized to give rise to van Have singularities near the Fermi energy $E_{\mathrm{F}}$, which induce a ferromagnetic (FM) order via the Stoner-type instability. This FM phase with broken time-reversal symmetry hosts the Weyl nodal lines near $E_{\mathrm{F}}$, which are converted into the multiple pairs of Weyl nodes by including spin-orbit coupling. Furthermore, we find that ${\mathrm{Y}}_2\mathrm{C}$ has a topologically nontrivial surface state near $E_{\mathrm{F}}$ as well as a tiny magnetic anisotropy energy, consistent with the observed surface state and paramagnetism at low temperatures below $\sim 2\mathrm{K}$. Our findings demonstrate the existence of Weyl fermions in a 2D electride material thereby providing a platform to study the interesting interplay of Weyl fermion physics and electride materials.

The level dynamics across the many-body localization transition is examined for XXZ spin model with a random magnetic field. We compare different scenarios of parameter-dependent motion in the system and consider measures such as level velocities, curvatures, as well as their fidelity susceptibilities. Studying the ergodic phase of the model we find that the level dynamics does not reveal the commonly believed universal behavior after rescaling the curvatures by the level velocity variance. At the same time, distributions of level curvatures and fidelity susceptibilities coincide with properly rescaled distributions for Gaussian orthogonal ensemble of random matrices. Profound differences exist depending on way the level dynamics is imposed in the many-body localized phase of the model in which the level dynamics can be understood with the help of local integrals of motion.

We discuss the approach toward equilibrium of an isolated quantum system. For a wide class of systems, in particular, for chaotic systems, we argue that the expectation value of a local operator averaged over a time interval of length $T$ is bounded by the so-called deviation function, which characterizes maximal deviation from the equilibrium of all states with a given value of energy fluctuations. This result applies to any initial state with a well-defined effective temperature. We provide numerical evidence that the bound is approximately saturated by the initial configurations with spatial inhomogeneities at a macroscopic level. In this way the deviation function establishes an explicit connection between the macroscopically observed timescales associated with the transport and the properties of microscopic matrix elements. The form of the deviation function indicates that among the “slowest” states which saturate the bound there are also those with arbitrarily long equilibration times.

Motivated by the recent experimental observation of the half-quantized thermal Hall conductivity for the candidate material of the Kitaev spin liquid, $\alpha \text{−}{\mathrm{RuCl}}_3$ [Y. Kasahara et al., Nature 559, 227 (2018)], we investigate effects of non-Kitaev exchange interactions, which exist in the real material, on the gapped chiral spin-liquid state realized in the case with an applied magnetic field. It is found that off-diagonal exchange interactions enhance significantly the mass gap of Majorana fermions. This result provides a possible explanation for robust quantization of the thermal Hall conductivity observed in the above-mentioned experiment. Furthermore, we demonstrate that if the Kitaev spin-liquid state and the zigzag antiferromagnetic order coexist around the border of these two phases, off-diagonal exchange interactions can induce Fermi surfaces of Majorana fermions, leading to a state similar to the U(1) spin liquid.

Periodic networks composed of capacitors and inductors have been demonstrated to possess topological properties with respect to incident electromagnetic waves. Here, we develop an analogy between the mathematical description of waves propagating in such networks and models of Majorana fermions hopping on a lattice. Using this analogy we propose simple electrical network architectures that realize Chern insulating phases for electromagnetic waves. Such Chern insulating networks have a bulk gap for a range of signal frequencies that is easily tunable and exhibit topologically protected chiral edge modes that traverse the gap and are robust to perturbations. The requisite time reversal symmetry breaking is achieved by including a class of weakly dissipative Hall resistor elements whose physical implementation we describe in detail.

The possible spin-polarized states of metallic jellium slabs have been studied by means of a Krieger-Li-Iafrate (KLI) approximation for the exchange potential. The stability of the different magnetic states has been determined by using a fixed-spin-moment method. Notably, in the search for solutions with different magnetizations, the KLI approximation leads to the sudden filling of electronic states for either majority or minority spin channels, and also to hysteresis effects, as the system crosses these points of discontinuity. These effects are completely missed by the local spin-density approximation (LSDA), which exhibits instead a continuous behavior. Close to the density corresponding to the Bloch instability of the homogeneous 3D electron gas, different exotic magnetic configurations appear, some of them featuring a spontaneous breaking of inversion symmetry around the slab center. As compared to the LSDA, the spin-dependent KLI approximation offers a moderate increase of the stability of a slab antiferromagnetic state.