We compute the low-energy excitation spectrum and the dynamical spin structure factor of the Kitaev-Heisenberg-Gamma model through a variational approach based on the exact fractionalized excitations of the pure Kitaev honeycomb model. This novel approach reveals the physical reason for the asymmetric stability of the Kitaev spin liquid phases around the ferromagnetic and antiferromagnetic Kitaev limits. Moreover, we demonstrate that the fractionalized excitations form bound states in specific regions of each Kitaev spin liquid phase and that certain phase transitions induced by Heisenberg and Gamma interactions are driven by the condensation of such a bound state. Remarkably, this bound state appears as a sharp mode in the dynamical spin structure factor, while its condensation patterns at the appropriate phase transitions provide a simple explanation for the magnetically ordered phases surrounding each Kitaev spin liquid phase.

We study the origin of the strong spin Hall effect (SHE) in a recently discovered family of Weyl semimetals, $\mathrm{LaAl}X$ ($X$ = Si, Ge) via first-principles with maximally localized Wannier functions. We show that the strong intrinsic spin Hall effect in $\mathrm{LaAl}X$ originates from the multiple slight anticrossings of nodal lines and points near to the Fermi energy due to their high-mirror symmetry and large spin-orbit interaction. It is further found that hole doping and increasing the temperature can enhance the spin Hall conductivity (${\sigma }_{\mathrm{SH}}$). However, the former also increases the electrical conductivity (${\sigma }_c$), while the latter decreases it. As a result, the independent tuning of ${\sigma }_{\mathrm{SH}}$ and ${\sigma }_c$ by increasing the temperature can enhance the spin Hall angle (proportional to $\frac{{\sigma }_{\mathrm{SH}}}{{\sigma }_c}$), a figure of merit of charge-to-spin current interconversion of spin-orbit torque devices. The underlying physics of such independent changes of the spin Hall and electrical conductivities by thermal means is revealed through the band-resolved and $k$-resolved spin Berry curvature. Our finding offers a way in the search of high spin Hall angle materials for room temperature spin-orbitronics applications.

We investigate the influence of general forms of disorder on the robustness of superconductivity in multiband materials. Specifically, we consider a general two-band system where the bands arise from an orbital degree of freedom of the electrons. Within the Born approximation, we show that the interplay of the spin-orbital structure of the normal-state Hamiltonian, disorder scattering, and superconducting pairing potentials can lead to significant deviations from the expected robustness of the superconductivity. This can be conveniently formulated in terms of the so-called “superconducting fitness.” In particular, we verify a key role for unconventional $s$-wave states, permitted by the spin-orbital structure and which may pair electrons that are not time-reversed partners. To exemplify the role of Fermi-surface topology and spin-orbital texture, we apply our formalism to the candidate topological superconductor ${\mathrm{Cu}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$, for which only a single band crosses the Fermi energy, as well as models of the iron pnictides, which possess multiple Fermi pockets.

We perform systematic first-principles calculations to investigate the spin-phonon coupling (SPC) mediated by spin-orbit coupling in pyrochlore ${\mathrm{Cd}}_2{\mathrm{Os}}_2{\mathrm{O}}_7$ which has the peculiar all-in-all-out noncollinear magnetic ground state. A large SPC coefficient up to $34\mathrm{c}{\mathrm{m}}^{–1}$ is found, showing the potential of using this material in thermal spin devices. We further split the SPC coefficients to contributions from symmetric exchange interaction, Dzyaloshinskii-Moriya interaction (DMI), and the single ion anisotropy. Unlike what was assumed in previous studies, the DMI contributions are rather important for most modes. These results provide insights for the understanding of the SPC in $5d$ transition metal oxides and useful guidance for the search of excellent spin caloritronic materials.

The $\mathrm{Hf}{\mathrm{Fe}}_6{\mathrm{Ge}}_6$-type $R{\mathrm{Mn}}_6{\mathrm{Sn}}_6$, a metallic system consisting of ferromagnetic kagome planes of Mn, has been recently shown to be a candidate hosting topological electronic properties. In this paper, we report magnetic and electronic properties in $\mathrm{Y}{\mathrm{Mn}}_6{\mathrm{Sn}}_{6-x}{\mathrm{Ga}}_x$ single crystals via magnetic susceptibility, electrical transport, and single-crystal neutron diffraction measurements. We show that the magnetic ground state of $\mathrm{Y}{\mathrm{Mn}}_6{\mathrm{Sn}}_{6-x}{\mathrm{Ga}}_x$ ($0\le x\le 0.61$) evolves from incommensurate antiferromagnet to ferromagnet with increasing Ga substitution $x$, a feature which is accompanied by the decrease in magnetoresistance. Furthermore, the topological Hall effect observed in the pristine compound is absent in the Ga-substituted ones; instead, the anomalous Hall effect persists which may be associated with the Berry curvature of gapped Dirac bands near the Fermi energy. These results suggest strong correlation between electronic properties and magnetism in this topological magnet that can be readily tuned via Ga substitution.

Quantum embedding based on the (one-electron-reduced) density matrix is revisited by means of the unitary Householder transformation. While being exact and equivalent to (but formally simpler than) density matrix embedding theory (DMET) in the noninteracting case, the resulting Householder-transformed density matrix functional embedding theory (Ht-DMFET) preserves, by construction, the single-particle character of the bath when electron correlation is introduced. In Ht-DMFET, the projected “$\mathrm{impurity}+\mathrm{bath}$” cluster's Hamiltonian (from which approximate local properties of the interacting lattice can be extracted) becomes an explicit functional of the density matrix. In the spirit of single-impurity DMET, we consider in this work a closed (two-electron) cluster constructed from the full-size noninteracting density matrix. When the (Householder-transformed) interaction on the bath site is taken into account, per-site energies obtained for the half-filled one-dimensional Hubbard lattice match almost perfectly the exact Bethe ansatz results in all correlation regimes. In the strongly correlated regime, the results deteriorate away from half-filling. This can be related to the electron number fluctuations in the (two-site) cluster which are neither described in Ht-DMFET nor in regular DMET. As expected, the per-site energies dramatically improve when increasing the number of embedded impurities. Formal connections with density/density matrix functional theories have been briefly discussed and should be explored further. Work is currently in progress in this direction.

The high Chern number phases with a Chern number $C>1$ have been observed in a recent experiment that was performed on the topological insulator (TI) multilayer structures, consisting of the alternating magnetic-doped and undoped TI layers. In this paper, we develop an effective method to determine the Chern numbers in the TI multilayer structures and then make a systematic study on the Chern number phase diagrams that are modulated by the magnetic doping and the middle-layer thickness. We point out that in the multilayer structure, the high-$C$ behavior can be attributed to the band inversion mechanisms. Moreover, we find that the lowest bands may be multifold degenerate around the $\mathrm{\Gamma }$ point, and when they are inverted, the Chern number change will be larger than 1. Besides the TI multilayer structures implemented in the experiment, we also explore the high-$C$ phase realizations in two other kinds of the TI multilayer structures. The implications of our results for experiments are discussed.

Using first-principles calculations, a class of Janus two-dimensional materials, $\mathrm{P}{A}_2\mathrm{As}$ ($A=\mathrm{Si}$, Ge, Sn, and Pb) monolayers, is predicted to be dynamically and thermally stable. The band gap of $\mathrm{P}{A}_2\mathrm{As}$ can be linearly modulated by external strain and electric field. The presence of the peculiar sombrero-type band in strained $\mathrm{P}{A}_2\mathrm{As}$ results in the intraband Lifshitz transition near the valence band top when including Rashba spin-orbit coupling. The energy range of intraband Lifshitz transition is linearly dependent on electric field, indicating potential electric control of the Fermi surface properties. In particular, hole doping leads to the ferromagnetic transition in $\mathrm{P}{A}_2\mathrm{As}$ due to Van Hove singularity and a divergence with $1/\sqrt{E}$ of the density of states. This ferromagnetism can be understood in terms of the Stoner criterion $D$($E_{\mathrm{F}}$)$I_{\mathrm{S}}>1$. A saturated magnetic moment of $1{\mu }_{\mathrm{B}}/\mathrm{hole}$ is obtained in hole-doped ${\mathrm{PSn}}_2\mathrm{As}$ and ${\mathrm{PPb}}_2\mathrm{As}$ with a wide range of hole densities. The highest Curie transition temperature $T_{\mathrm{c}}$ is estimated to be 93.5 K at the mean field level. We demonstrate that hole density and tensile strain are two effective approaches to control the Stoner ferromagnetism in practical applications. Moreover, various electronic transitions, such as semiconductor to half-metal, half-metal to metal, and semiconductor to metal, are revealed in hole-doped $\mathrm{P}{A}_2\mathrm{As}$. Finally, we explore the feasibility of realizing ferromagnetism by introducing $p$-type dopants and defects. The experimentally controlled intraband Lifshitz transition and Stoner ferromagnetism demonstrate that Janus $\mathrm{P}{A}_2\mathrm{As}$ monolayers have a wide application potential in future electronic and spintronic devices.

Two-dimensional lattices are an important stage for studying many aspects of quantum physics, in particular the topological phases. The valley Hall and anomalous Hall effects are two representative topological phenomena. Here we show that they can be unified in a strained honeycomb lattice, where the hopping strengths between neighboring sites are designed by mimicking those between the Fock states in a three-mode Jaynes-Cummings model. Such a strain induces an effective magnetic field, which results in quantized Landau levels. The eigenstates in the zeroth Landau level can be represented by the eigenstates of a large pseudo-spin. We find that the valley Hall current and the chiral edge current in the Haldane model correspond to the pseudo-spin precession around different axes. Our study sheds light on connection between seemingly unrelated topological phases in condensed matter physics.

We present a theoretical investigation of electron states hosted by magnetic domain walls on the three-dimensional topological insulator surface. The consideration includes the domain walls with distinct vectorial and spatial textures. The study is carried out on the basis of the Hamiltonian for quasirelativistic fermions by using a continual approach and tight-binding calculations. We derive the spectral characteristics and spatial localization of the one-dimensional low-energy states appearing at the domain walls. The antiphase domain walls are shown to generate the topologically protected chiral states with linear dispersion, the group velocity and spin-polarization direction of which depend on an easy-axis orientation. In the case of an easy-plane anisotropy, we predict a realization of a dispersionless state flatband in the energy spectrum, that is spin polarized along the surface normal. Modification of the surface states in the multidomain case, which is approximated by a periodic set of domain walls, is described as well. We find that the magnetic domain walls with complex internal texture, such as Néel-like or Bloch-like walls, also host the topological states, although their spectrum and spin structure can be changed compared with the sharp wall case.

Sequential plateau transitions of quantum spin chains ($S=1$, 3/2, 2, and 3) are demonstrated by a spin pump using dimerization and a staggered magnetic field as synthetic dimensions. The bulk is characterized by the Chern number associated with the boundary twist and the pump protocol as the time. It counts the number of critical points in the loop that is specified by the $Z_2$ Berry phases. With an open boundary condition, the discontinuity of the spin weighted center of mass due to emergent effective edge spins also characterizes the pump as the bulk-edge correspondence. It requires extra level crossings in the pump as a superselection rule that is consistent with the valence bond solid picture.

Bilinear magnetoresistance (BMR), the magnetoresistance that is linear against either magnetic field or applied current, is a hot topic of recent investigations. While most of the previous works focused on isotropic BMR, here we report on a strongly anisotropic BMR for (110) $\mathrm{SrTi}{\mathrm{O}}_3$-based two-dimensional electron gas (2DEG). Remarkably, the BMR measured along the [001] axis can be fivefold as large as that obtained along the $\left[1\overline{1}0\right]$ axis. A close relation is found between BMR and current-induced effective Rashba field, and it is the anisotropy of the Rashba field that causes the anisotropic BMR. Based on the analysis of anisotropic magnetoresistance, effective Rashba fields up to 4.5 T are determined. The band structure of the 2DEG is further calculated, ellipse-shaped Fermi rings are obtained, and the respective effects of different Fermi rings on BMR are distinguished. This work demonstrates the great potential of anisotropic 2DEG for the exploration of unusual effects.

The emerging and screening of local magnetic moments in solids have been investigated for more than 60 years. Local vacancies as in graphene or in heavy fermions can induce decoupled bound states that lead to the formation of local moments. In this paper, we address the puzzling question how these local moments can be screened and what determines the additionally emerging low-temperature scale. We review the initial problem for half-filled conduction bands from two complementary perspectives: By a single-particle supercell analysis in the uncorrelated limit and by the Lieb-Mathis theorem for systems with a large Coulomb interaction $U$. Applying Wilson's numerical renormalization group approach to a recently developed mapping of the problem onto an effective low-energy description of a Kondo hole with up to $N_f=7$ correlated impurities as background, we proof that the stable local moments are subject to screening by three different mechanisms. Firstly the local moments are delocalized by a finite $U$ beyond the single-particle bound state. We find a Kosterlitz-Thouless type transition governed by an exponentially suppressed low-energy scale of a counterintuitive Kondo form with $J_{\mathrm{eff}}\propto U^n$ for small $U$, where $n>1$ depends on the precise model. Secondly, we show that away from half-filling the local moment phase becomes unstable and is replaced by two types of singlet phases that are adiabatically connected. At a critical value for the band center, the physics is governed by an exponentially suppressed Kondo scale approaching the strong coupling phase that is replaced by a singlet formation via antiferromagnetic RKKY interaction for large deviation from the critical values. Thirdly, we show that the local magnetic moment can be screened by a Kondo hole orbital at finite energy, even though the orbital occupation is negligible: An additional low-energy scale emerges below which the localized moment is quenched. Similarities to the experimental findings in ${\mathrm{Ce}}_{1-x}{\mathrm{La}}_x{\mathrm{Pd}}_3$ are pointed out.

Disorder or interactions can turn metals into insulators. One of the simplest settings in which to study this physics is given by the Falikov-Kimball (FK) model, which describes itinerant fermions interacting with a classical Ising background field. Despite the translational invariance of the model, inhomogeneous configurations of the background field give rise to effective disorder physics which lead to a rich phase diagram in two (or more) dimensions with finite-temperature charge-density wave (CDW) transitions and interaction-tuned Anderson versus Mott localized phases. Here, we propose a generalized FK model in one dimension with long-range interactions which shows a similarly rich phase diagram. We use an exact Markov chain Monte Carlo method to map the phase diagram and compute the energy-resolved localization properties of the fermions. We compare the behavior of this transitionally invariant model to an Anderson model of uncorrelated binary disorder about a background CDW field which confirms that the fermionic sector only fully localizes for very large system sizes.

In this Letter, we introduce a paradigm to realize magnetomechanical metastructures inspired by multilayer two-dimensional materials, such as graphene bilayers. The metastructures are intended to capture two aspects of their nanoscale counterparts. One is the multilayer geometry, which is implemented by stacking hexagonal lattice sheets. The other is the landscape of weak interlayer forces, which is mimicked by the interactions between pairs of magnets located at corresponding lattice sites on adjacent layers. We illustrate the potential of this paradigm through a three-layer prototype. The two rigid outer lattices serve as control layers, while the thin inner layer is free to experience flexural motion under the confining action of the magnetic forces exchanged with the outer ones, thus behaving as a lattice on an elastic foundation. The inner layer is free to rotate relative to the others, giving rise to a rich spectrum of interlayer interaction patterns. Our objective is to determine how the dynamical response can be tuned by changing the twist angle between the layers. Specifically, we demonstrate experimentally that switching between different stacking patterns has profound consequences on the phonon landscape, opening and closing band gaps in different frequency regimes.

We demonstrate the phase shift of the Rayleigh-type surface acoustic wave (RSAW) in a ferromagnetic ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$ film based on the gyromagnetic Einstein–de Haas (EdH) torque that can be attributed to the back action of spin-wave excitation. The EdH torque modulates the transverse velocity of the bulk acoustic wave that causes the bipolar phase shift of RSAW. When compared with a magnetoelastic torque, the phase shift can be more prominently enhanced by increasing the frequency. The gyromagnetic torque in the RSAW paves the way for controlling spin-mechatronics devices without magnetoelastic torque which is specific to a certain material.

We investigated the nature of the quasiparticle state in the vortex core by means of the flux-flow Hall effect measurements at 15.8 GHz. We measured the flux-flow Hall effect in cuprate superconductors, ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_y$ and ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_y$ single crystals, whose equilibrium $B\text{−}T$ phase diagrams were different. As a result, we found that the Hall angle is independent of the magnetic field, and reaches an order of unity at low temperatures in BSCCO. However, in YBCO, the angle increases with increasing magnetic field even at low temperatures. We understood that this difference in the magnetic field dependence of the Hall angle is due to the difference in the influence of the pinning, which originated from the difference in the vortex state (liquid vs. solid) between the two materials. However, as a common feature, both materials showed a large tangent of the Hall angle at low temperatures, which was larger by an order of magnitude than those obtained in the effective viscous drag coefficient measurements. We discussed the origin of the discrepancy both in terms of the possible nonlinearity of the viscous drag force and possible hidden dissipation mechanisms. The unexpectedly large Hall angle of the vortex motion in cuprates revealed in our flux-flow Hall effect study poses a serious question on the fundamental understanding of the motion of the quantized vortex in superconductors, and it deserves further investigation.

Topological physics of phonon spectra has been attracting great interest. Using the first-principle calculations and symmetry analysis, we show the realistic ternary nitride ${\mathrm{Li}}_6{\mathrm{WN}}_4$ features ideal (nearly flat) nodal-surface and nodal-line structures in its phonon spectra. These nodal degeneracies are shaped like lanterns, and their existence is guaranteed by nonsymmorphic symmetry. The corresponding topological phonon surface state covers exactly half the surface Brillouin zone and can thereby be distinguished from those of conventional nodal-line and nodal-surface semimetals. Our study enriches the classification of topological quantum phases, predicts ideal material candidates, and provides a good platform for investigating the interaction between nodal-line and nodal-surface phonons.