We show that a sliding motion between the two layers of a moiré superlattice induces an electric current and realizes a two-dimensional version of the topological Thouless pump when the Fermi energy lies in one of the minigaps. Interestingly, a chiral charge pump, namely, a transverse current induced by the sliding motion, is possible in twisted homobilayers. This result is confirmed by a concrete calculation of the adiabatic current in twisted bilayer graphene. Our work reveals an interesting link between mechanical motion and electricity unique to moiré superlattices, and may find applications in nanogenerators and nanomotors.

The energy spectra for the tight-binding models on the Lieb and kagome lattices both exhibit a flat band. We study a model which continuously interpolates between these two limits. The flat band located in the middle of the three-band spectrum for the Lieb lattice is distorted, generating two pairs of Dirac points. While the upper pair evolves into graphenelike Dirac cones in the kagome limit, the low-energy pair evolves until it merges, producing the band-bottom flat band. The topological characterization of the Dirac points is achieved by projecting the Hamiltonian on the two relevant bands in order to obtain an effective Dirac Hamiltonian. The low-energy pair of Dirac points is particularly interesting: when they emerge, they have opposite winding numbers, but as they merge, they have the same winding number. This apparent paradox is due to a continuous rotation of their states in pseudospin space, characterized by a winding vector. This simple, but quite rich model, suggests a way to a systematic characterization of two-band contact points in multiband systems.

Universal properties of a critical quantum spin chain are encoded in the underlying conformal field theory (CFT). This underlying CFT is fully characterized by its conformal data. We propose a method to extract the conformal data from a critical quantum spin chain with both periodic and antiperiodic boundary conditions (PBC and APBC) based on low-energy eigenstates, generalizing previous work on spin chains with only PBC. First, scaling dimensions and conformal spins are extracted from the energies and momenta of the eigenstates. Second, the Koo-Saleur formula of lattice Virasoro generators is generalized to APBC and used to identify conformal towers. Third, local and string operators on the lattice are identified with CFT operators with PBC and APBC, respectively. Finally, operator product expansion coefficients are extracted by computing matrix elements of lattice primary operators in the low-energy subspaces with PBC and APBC. To go beyond exact diagonalization, tensor network methods based on periodic uniform matrix product states are used. We illustrate our approach with critical and tricritical Ising quantum spin chains. In the latter case, we propose lattice operators that correspond to super-Virasoro generators and verify their action on low-energy eigenstates. In this way, we explore the emergence of superconformal symmetry in the quantum spin chain.

Using classical molecular dynamics simulations and the virial description of atomic stress, this paper reveals that effective toughness and strength in defective diamond nanowires (NWs) are governed by the geometric confinement of atoms at the critical sites of the NWs. Results suggest existence of five characteristic regimes in defective NWs under applied deformation. They include the defective regime, the surface regime, the core regime, the surface-core intersection regime, and the defect-core intersection regime. The defective regime and the surface regime soften the NW and carry the maximum angular deformation at the expense of breaking local symmetry of atomic structure. On the other hand, the intersecting regimes tend to preserve the symmetry, carry the most aggressive linear deformation, and act as the critical sites for localization of atomic stress. In the defect-core intersecting regime, the differential response of its neighboring regimes to linear and angular deformations as well as the elastic fields emanating from its critical sites impose an intricate effect comprising geometric confinement and propensity to retain local symmetry. Consequently, the highest localization of elastic energy and atomic stress takes place at the critical sites of the defect-core regime and it controls the effective toughness and strength behavior of the defective nanowires. Although size-dependent variation in strength and toughness is controlled primarily by surface softening, defect-induced alteration of strength and toughness is governed by the geometric confinement. Furthermore, an atomistic analysis reveals that the localized stress fields grow radially outward from the defective regime for defective NWs, whereas in defect-free NWs they evolve inward from the surface.

The crystal structures and properties of boron-silicon (B-Si) compounds under pressure have been systematically explored using particle swarm optimization structure prediction method in combination with first-principles calculations. Three new stoichiometries, ${\mathrm{B}}_2\mathrm{Si}$, BSi, and ${\mathrm{BSi}}_2$, are predicted to be stable gradually under pressure, where increasing pressure favors the formation of silicon rich B-Si compounds. In the boron-rich compounds, the network of boron atoms changes from ${\mathrm{B}}_{12}$ icosahedron in the ambient phases to the similar buckled graphenelike layers in the high-pressure phases, which crystalize in the same $P\overline{3}m1$ symmetry but with different numbers of boron layers between adjacent silicon layers. Phonon calculations show that these structures might be retained to ambient conditions as metastable phases. Further electron-phonon coupling calculations indicate that the high-pressure phases of boron-rich compounds might superconduct at 1 atm, with the highest $T_c$ value of 21 K from the Allen-Dynes equation in $P\overline{3}m1$ ${\mathrm{B}}_2\mathrm{Si}$, which is much higher than the one observed in boron doped diamond-type silicon. Moreover, further fully anisotropic Migdal-Eliashberg calculations indicate that ${\mathrm{B}}_2\mathrm{Si}$ is a two-gap anisotropic superconductor and the estimated $T_c$ might reach up to 30 K at 1 atm. On the silicon-rich side, ${\mathrm{BSi}}_2$ is predicted to be stable in the ${\mathrm{CuAl}}_2$-type structure. Our current results significantly enrich the phase diagram of the B-Si system and will stimulate further experimental study.

Magnetic domain walls in nanowires behave as particles interacting through the exchange field. As topological objects, their interaction is determined by their chirality or topological charge. We investigate analytically the topological repulsion between magnetic domain walls with the same topological charge in nanostripes (with easy-plane magnetization) and show that it decays algebraically as $r^{-2}$, being part of a larger class of interactions that produce topological long-range order in two dimensions. We compare the topological repulsion between the walls with other types of fundamental interactions with exponential spatial decay, such as the Yukawa-Reid potential, and with micromagnetic simulations. We determine that trains of such walls can be well described analytically and can be displaced regularly in nanowires leading to practical applications.

Recently the hybridization of microwave-frequency cavity modes with collective spin excitations has attracted large interest for the implementation of quantum computation protocols, which exploit the transfer of information among these two physical systems. Here we investigate the interaction among the magnetization precession modes of a small yttrium iron garnet sphere and the microwave electromagnetic modes, resonating in a tridimensional aluminum cavity. In the strong coupling regime, anticrossing features were observed corresponding to various magnetostatic modes, which were excited in a magnetically saturated sample. Time-resolved studies show evidence of Rabi oscillations, demonstrating coherent exchange of energy among photonic and magnon modes. To facilitate the analysis of the standing spin-wave patterns, we propose here a procedure, based on the introduction of a scaling variable. The resulting easier identification of magnetostatic modes can be exploited to investigate, control, and compare many-level hybrid systems in cavity- and opto-magnonics research.

All known quasi-two-dimensional ferromagnets, such as $(X=\mathrm{Br},\mathrm{I})$ or ${\mathrm{Cr}}_2{(\mathrm{Ge},\mathrm{Si})}_2{\mathrm{Te}}_6$, exhibit a peculiar temperature dependence of the magnetization under small magnetic fields applied in the hard plane. Investigating the van der Waals layered ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$ by magnetization and specific-heat measurements under magnetic fields, we report the temperature dependence of the effective magnetic anisotropy as a plausible explanation for this unusual behavior. Magnetic temperature-field phase diagrams were measured for magnetic fields applied along the magnetic easy axis and in the hard plane up to 30 kOe and 150 K to obtain a detailed understanding of the magnetization behavior in the low-field region and especially below the magnetic saturation fields. From these magnetic phase diagrams the temperature dependence of the effective magnetocrystaline anisotropy constant is extracted and compared to the corresponding theory, unique for ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$ until now. Based on the thermal evolution of the effective magnetocrystalline anisotropy constant and the aforementioned magnetic phase diagrams, a qualitative scheme is developed explaining the changes of magnetization direction due to the influence of temperature, as well as strength and direction of external magnetic fields in ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$. Structural and magnetic similarities to other quasi-two-dimensional ferromagnets may allow this scheme to be generalized for the whole class of materials.

High-resolution resonant inelastic x-ray scattering measurements ($\mathrm{\Delta }E=46\mathrm{meV}$) have been performed on ${\mathrm{Cd}}_2{\mathrm{Os}}_2{\mathrm{O}}_7$ through the metal-to-insulator transition (MIT). A magnetic excitation at 125 meV evolves continuously through the MIT, in agreement with recent Raman-scattering results, and provides further confirmation for an all-in all-out magnetic ground state. Asymmetry of this feature is likely a result of coupling between the electronic and the magnetic degrees of freedom. We also observe a broad continuum of interband excitations centered at 0.3 eV energy loss. This is indicative of significant hybridization between Os $5d$ and O $2p$ states and the concurrent itinerant nature of the system. In turn, this suggests a possible breakdown of the free-ion model for ${\mathrm{Cd}}_2{\mathrm{Os}}_2{\mathrm{O}}_7$.

Detecting chiral edge modes in topological materials has been intensively pursued in experiments. However, the phenomena caused by the modes are not yet elucidated theoretically. We study the dynamics of chiral spinon wave packets at the edge in Kitaev-type magnets. More precisely, by relying on the exact solvability of the models, we construct a spinon wave packet, localized edge magnetization, which shows oriented propagation along the edge, whose behavior is expected from the chiral character of the dispersion relation of the chiral edge modes. In general, this approach enables us to study not only spin transport in anisotropic magnets but also charge transport in Bogoliubov–de Gennes-type superconductors because it does not rely on a conserved quantity.

Using single-crystal neutron diffraction, we present a systematic investigation of the crystal structure and magnetism of the van der Waals topological insulators ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ and ${\mathrm{MnBi}}_4{\mathrm{Te}}_7$, where rich topological quantum states have been recently predicted and observed. Structural refinements reveal that considerable Bi atoms occupied on the Mn sites in both materials, distinct from the previously reported antisite disorder. We show unambiguously that ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ orders antiferromagnetically below 24 K, featured by a magnetic symmetry $R_I\text{−}3c$, while ${\mathrm{MnBi}}_4{\mathrm{Te}}_7$ is antiferromagnetic below 13 K with a magnetic space group $P_c\text{−}3c1$. They both present antiferromagnetically coupled ferromagnetic layers with spins along the $c$ axis. We put forward a stacking rule for the crystal structure of an infinitely adaptive series ${\mathrm{MnBi}}_{2n}{\mathrm{Te}}_{3n+1}$ ($n\ge 1$) with a building unit of $\left[{\mathrm{Bi}}_2{\mathrm{Te}}_3\right]$. By comparing the magnetic properties between ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ and ${\mathrm{MnBi}}_4{\mathrm{Te}}_7$, together with recent density-functional theory calculations, we concluded that a two-dimensional magnetism limit might be realized in the derivatives. Our work may promote theoretical studies of topological magnetic states in the series of ${\mathrm{MnBi}}_{2n}{\mathrm{Te}}_{3n+1}$.

X-ray scattering and magnetization measurements have been used to explore the extent of orbital molecule formation in a variety of $A{\mathrm{V}}_2{\mathrm{O}}_4$ vanadium oxide spinels. Zn doping suppresses the long-range order of trimer-tetramer pairs that occurs in $\mathrm{Ga}{\mathrm{V}}_2{\mathrm{O}}_4$, but disordered orbital molecules are found across most of the $\mathrm{Z}{\mathrm{n}}_x\mathrm{G}{\mathrm{a}}_{1-x}{\mathrm{V}}_2{\mathrm{O}}_4$ series ($0.06\le x<0.875$). Orbital molecules are not observed in the ground states of $\mathrm{Zn}{\mathrm{V}}_2{\mathrm{O}}_4, \mathrm{Mg}{\mathrm{V}}_2{\mathrm{O}}_4$, or $\mathrm{Li}{\mathrm{V}}_2{\mathrm{O}}_4$ but are likely present in $\mathrm{L}{\mathrm{i}}_{0.5}\mathrm{G}{\mathrm{a}}_{0.5}{\mathrm{V}}_2{\mathrm{O}}_4$, an analog of the former two materials. The ratio of observed to ideal values of the V-V nearest-neighbor distance has been used to rationalize these observations.

We study out-of-time-ordered correlators (OTOC) in a free fermionic model with a quasiperiodic potential. This model is equivalent to the Aubry-André model and features a phase transition from an extended phase to a localized phase at a nonzero value of the strength of the quasiperiodic potential. We investigate five different time regimes of interest for out-of-time-ordered correlators: early, wave front, $x=v_{B}t$, late time equilibration, and infinite time. For the early time regime we observe a power law for all potential strengths. For the precursor time regime preceding the wave front we confirm a recently proposed universal form and use it to extract the characteristic velocity of the wave front for the present model. A Gaussian waveform is observed to work well in the time regime surrounding $x=v_{B}t$, the wave front arrival time. Our main result is for the late time equilibration regime where we derive a finite time equilibration bound for the OTOC, bounding the correlator's distance from its late time value. The bound impose strict limits on equilibration of the OTOC in the extended regime and is valid not only for the Aubry-André model but for any quadratic model. Finally, momentum out-of-time-ordered correlators for the Aubry-André model are studied where large values of the OTOC are observed at late times at the critical point.

The local atomic and magnetic structures of the compounds $A{\mathrm{MnO}}_2$ ($A$ = Na, Cu), which realize a geometrically frustrated, spatially anisotropic triangular lattice of Mn spins, have been investigated by atomic and magnetic pair distribution function analysis of neutron total scattering data. Relief of frustration in ${\mathrm{CuMnO}}_2$ is accompanied by a conventional cooperative symmetry-lowering lattice distortion driven by Néel order. In ${\mathrm{NaMnO}}_2$, however, the distortion has a short-range nature. A cooperative interaction between the locally broken symmetry and short-range magnetic correlations lifts the magnetic degeneracy on a nanometer length scale, enabling long-range magnetic order in the Na derivative. The degree of frustration, mediated by residual disorder, contributes to the rather differing pathways to a single, stable magnetic ground state in these two related compounds. This study demonstrates how nanoscale structural distortions that cause local-scale perturbations can lift the ground-state degeneracy and trigger macroscopic magnetic order.

We report muon spin relaxation rate measurements on films composed of aluminum grains having a size of a few nm, with a large energy level splitting of the order of 100 K. The films range from weakly metallic to insulating. In the insulating case, the low-temperature relaxation rate is consistent with the presence of single electron spins in grains having an odd number of electrons, known as Kubo spins. The relaxation rate temperature dependence follows an activation law having an energy scale in agreement with the average level splitting. In weakly metallic films, inter-grain junction spins may contribute substantially to the smaller relaxation rate.

We present a theoretical calculation of the pressure-temperature-field phase diagram for the vortex phases of rotating superfluid ${}^3\mathrm{He}\text{−}\mathrm{B}$. Based on a strong-coupling Ginzburg-Landau functional that accounts for the relative stability of the bulk A and B phases of ${}^3\mathrm{He}$ at all pressures, we report calculations for the internal structure and free energies of distinct broken-symmetry vortices in rotating superfluid ${}^3\mathrm{He}\text{−}\mathrm{B}$. Theoretical results for the equilibrium vortex phase diagram in zero field and an external field of $H=284\text{G}$ parallel to the rotation axis, $\mathbf{H}\parallel \mathit{\Omega }$, are reported, as well as the supercooling transition line, $T_{\text{V}}^{*}(p,H)$. In zero field the vortex phases of ${}^3\mathrm{He}\text{−}\mathrm{B}$ are separated by a first-order phase transition line $T_{\text{V}}\left(p\right)$ that terminates on the bulk critical line $T_c\left(p\right)$ at a triple point. The low-pressure, low-temperature phase is characterized by an array of singly quantized vortices that spontaneously breaks axial rotation symmetry, exhibits anisotropic vortex currents and an axial current anomaly (D-core phase). The high-pressure, high-temperature phase is characterized by vortices with both bulk A phase and $\beta$ phase in their cores (A-core phase). We show that this phase is metastable and supercools down to a minimum temperature, $T_{\text{V}}^{*}(p,H)$, below which it is globally unstable to an array of D-core vortices. For $H\gtrsim 60\text{G}$ external magnetic fields aligned along the axis of rotation increase the region of stability of the A-core phase of rotating ${}^3\mathrm{He}\text{−}\mathrm{B}$, opening a window of stability down to low pressures. These results are compared with the experimentally reported phase transitions in rotating ${}^3\mathrm{He}\text{−}\mathrm{B}$.

We investigate a symmetry-protected $Z_2$ topological electron glass, a glassy equivalent of the $Z_2$ topological band insulator in crystalline systems, and uncover associated quantum phase transitions in this three-dimensional amorphous network of atoms. Through explicit numerical calculations of the Witten effect, we show that the $Z_2$ glass is characterized by an anomalous electromagnetic response, i.e., it can host dyons with $\frac{1}{2}$ electronic charge. We further study, using a variety of numerical diagnostics including such electromagnetic responses, the phase transitions of the $Z_2$ glass into a metallic and/or a trivial insulating phase. We find that the phase transitions here are governed by subtle features of mobility edges and “spectral inversion” which are possibly unique to structurally amorphous systems. Our results provide a concrete setting to understand the general underpinnings of such phases, where strong structural disorder interplays with symmetry-protected topological order.

We introduce a nested optimization procedure using semidefinite relaxation for the fitting step in Hamiltonian-based cluster dynamical mean-field theory methodologies. We show that the proposed method is more efficient and flexible than state-of-the-art fitting schemes, which allows us to treat as large a number of bath sites as the impurity solver at hand allows. We characterize its robustness to initial conditions and symmetry constraints, thus providing conclusive evidence that in the presence of a large bath our semidefinite relaxation approach can find the correct set of bath parameters without needing to include a priori knowledge of the properties that are to be described. We believe this method will be of great use for Hamiltonian-based calculations, simplifying and improving one of the key steps in cluster dynamical mean-field theory calculations.

Efficient ab initio calculations of correlated materials at finite temperatures require compact representations of the Green's functions both in imaginary time and in Matsubara frequency. In this paper, we introduce a general procedure which generates sparse sampling points in time and frequency from compact orthogonal basis representations, such as Chebyshev polynomials and intermediate representation basis functions. These sampling points accurately resolve the information contained in the Green's function, and efficient transforms between different representations are formulated with minimal loss of information. As a demonstration, we apply the sparse sampling scheme to diagrammatic $GW$ and second-order Green's function theory calculations of a hydrogen chain of noble gas atoms and of a silicon crystal.

We report the magnetoresistance (MR) and de Haas-van Alphen (dHvA) effect studies of single crystal ${\mathrm{HfTe}}_2$, which is predicted to be a Dirac material. The MR of ${\mathrm{HfTe}}_2$ exhibits unsaturated quadratic behavior and follows Kohler's rule. Anisotropic MR with twofold symmetry has been observed by rotating the magnetic field along different directions. Furthermore, we have performed the measurements of magnetization and observed the dHvA-type oscillation. Two oscillation frequencies and the corresponding Fermi surfaces are identified from the analysis of the oscillation.