Majorana fermions subject to the non-Abelian braid group are believed to be the basic ingredients of future topological quantum computations. In this work, we propose to simulate Majorana fermions of the Kitaev model in electric circuits based on the observation that the circuit Laplacian can be made identical to the Hamiltonian. A set of AC voltages along the chain plays the role of the wave function. We generate an arbitral number of topological segments in a Kitaev chain. A pair of topological edge states emerge at the edges of a topological segment. Its wave function is observable by the position and the phase of a peak in impedance measurement. It is possible to braid any pair of neighboring edge states with the aid of T-junction geometry. By calculating the Berry phase acquired by their eigenfunctions, the braiding is shown to generate one-qubit and two-qubit unitary operations. We explicitly construct Clifford quantum gates based on them. We also present an operator formalism by regarding a topological edge state as a topological soliton intertwining the trivial segment and the topological segment. Our analysis shows that the electric-circuit approach can simulate the Majorana-fermion approach to topological quantum computations.

Manipulating interlayer magnetic coupling (IMC) of van der Waals (vdW) magnets is the key to tailoring material properties for various electronic applications and fundamental studies. Using $\mathrm{Mn}{\mathrm{Bi}}_2{\mathrm{Te}}_4$-family materials as examples, we systematically investigate the constituent-element dependence of IMC by first-principles calculations and attribute the IMC to unusual long-range superexchange interactions mediated by the $p$ orbitals across the vdW gap. Remarkably, a simple, universal rule is proposed to determine the sign of IMC (ferromagnetic or antiferromagnetic) by $d$-orbital occupation, and guidance is provided to achieve extraordinarily strong or stacking-dependent IMC by element engineering. Furthermore, several magnetic topological states are designed by heterostructuring, including ferromagnetic Weyl semimetals, high-order topological insulators, and unusual kinds of quantum anomalous Hall insulators. The findings enable us to engineer the magnetic and topological properties of $\mathrm{Mn}{\mathrm{Bi}}_2{\mathrm{Te}}_4$-family materials as well as other vdW magnetic materials and heterostructures.

The pairing glue of high-$T_{\mathrm{c}}$ superconductivity in heavily electron-doped (e-doped) FeSe, in which hole pockets are absent, has been an important unsolved problem. Here, we focus on a heavily e-doped bulk superconductor ${\mathrm{Li}}_{1-x}{\mathrm{Fe}}_x\mathrm{OHFeSe}$ $(T_{\mathrm{c}}\sim 40\mathrm{K})$. We construct a multiorbital model beyond the rigid band approximation and analyze the spin and orbital fluctuations by taking both vertex corrections (VCs) and self-energy into consideration. Without e-doping ($x=0$), the ferro-orbital order without magnetism in FeSe is reproduced by the VCs. The orbital order quickly disappears when the hole pocket vanishes at $x\sim 0.03$. With increasing $x$ further, the spin fluctuations remain small, whereas orbital fluctuations gradually increase with $x$ due to the VCs. The negative feedback due to the self-energy is crucial to explain experimental phase diagram. Thanks to both vertex and self-energy corrections, the orbital-fluctuation-mediated $s_{++}$-wave state appears for a wide doping range, consistent with experiments.

While $\mathbf{k}·\mathbf{p}$ Hamiltonians are frequently used for the description of electronic states in quantum nanostructures, a method is lacking to obtain them in their symmetrized form directly from ab initio band structure calculations of bulk material. We developed a method for obtaining the parameters and the symmetry-adapted form of the $\mathbf{k}·\mathbf{p}$ Hamiltonian from the output of an ab initio band structure calculation. The method consists of (i) evaluation of momentum matrix elements between the wave functions obtained from band structure calculation; (ii) identification of the unitary transformation that transforms these wave functions to the symmetry-adapted basis; (iii) transformation of the $\mathbf{k}·\mathbf{p}$ Hamiltonian to the symmetry-adapted basis. We illustrate the methodology by obtaining $\mathbf{k}·\mathbf{p}$ Hamiltonians that describe the band structure of zinc-blende CdSe and then we use the Hamiltonians obtained to calculate the electronic states in CdSe quantum wells. Excellent agreement between density functional theory and $\mathbf{k}·\mathbf{p}$ is obtained for the electronic structure, even for quite thin wells.

We investigate the interacting, one-dimensional Rice-Mele model, a prototypical fermionic model of topological properties. To set the stage, we first compute the single-particle spectral function, the local density, and the boundary charge in the absence of interactions. We find that the fractional part of the boundary charge is fully determined by bulk properties of the lattice model. In a large parameter regime the boundary charge agrees with the one obtained from an effective low-energy theory (arXiv:2004.00463). Second, we investigate the robustness of our results towards two-particle interactions. To resume the series of leading logarithms for small gaps, which dismantle plain perturbation theory in the interaction, we use an essentially analytical renormalization group approach. It is controlled for small interactions and can directly be applied to the microscopic lattice model. We benchmark the results against numerical density matrix renormalization group data. The main interaction effect in the bulk is a power-law renormalization of the gap with an interaction dependent exponent. The important characteristics of the fractional part of the boundary charge are unaltered and can be understood from the renormalized bulk properties. This requires a consistent treatment not only of the low-energy gap renormalization but also of the high-energy band width one. In contrast to low-energy field theories our renormalization group approach also provides the latter. We show that the interaction spoils the relation between the bulk properties and the number of edge states, consistent with the observation that the Rice-Mele model with finite potential modulation does not reveal any zero-energy edge states.

We investigate the transport features of a planar Josephson junction which was recently proposed and verified as a host of Majorana bound states (MBSs). With finite phase difference, MBSs can be gapped from the excited states at moderate Zeeman field. A considerable amount of current density develops at the stripe edges due to the presence of the MBSs. More interestingly, we note that in detecting MBSs via scanning tunneling spectroscopy (STM), a conductance minimum is observed at the peak position of the MBS local density of states. We ascribe this discrepancy to the fact that the penetration of the pair potential decays away the superconducting/normal interface. These results are instructive in not only for identifying MBSs in planar Josephson junction via STM measurement, but also for the detection of MBSs in platforms with nonuniform pair potentials.

The dice lattice supports Aharonov-Bohm caging when all the energy bands are flat for the half-quantum magnetic flux enclosed in each plaquette of the lattice. We analytically investigate the eigenstates and discuss the localization dynamics. We find that arbitrary excitation is compactly confined within the excited-site-related snowflake structures of the dice lattice; as a consequence that the nonzero-energy flatband localizes in the single snowflake, whereas the zero-energy flatband localizes in three nearest snowflakes that are connected in the form of a trident star. The localization dynamics of an arbitrary excitation is grasped from two dynamical behaviors of single-site excitation. For the single-site excitation at the center of a snowflake, the excitation is localized in that snowflake; whereas for the single-site excitation at the branch site of a snowflake, the excitation is localized in the three snowflakes that the branch site belongs to. Our findings deepen the understanding of destructive interference and the dynamics of Aharonov-Bohm caging in the dice lattice.

We have used numerical micromagnetic simulations to propose a feasible candidate system in which Bloch oscillations of spin waves could be observed experimentally. Our simulations demonstrate these phenomena for backward volume magnetostatic spin waves (BVMSWs) in a film of yttrium-iron-garnet in a spatially varying bias magnetic field comprising a sinusoidal and gradient contributions. Despite the complex character of the BVMSW dispersion relation, the spin-wave packets are distinctly confined by the field gradient, while showing only minor broadening over the simulation time.

We examine the thermalization/localization trade off in an interacting and disordered Kitaev model, specifically addressing whether signatures of many-body localization can coexist with the systems topological phase. Using methods applicable to finite size systems (e.g., the generalized one-particle density matrix, eigenstate entanglement entropy, inverse zero modes coherence length), we identify a regime of parameter space in the vicinity of the noninteracting limit where topological superconductivity survives together with a significant violation of the eigenstate-thermalization hypothesis (ETH) at finite energy densities. We further identify that the coexistence regime features an anomalous behavior of the von Neumann entanglement entropy as a function of disorder strength, which we attribute to competing ETH violation mechanisms. At low disorder, prethermalization like effects that occur due to lack of hybridization between high-energy eigenstates reflect an approximate particle conservation law. In this regime the system tends to thermalize to a generalized Gibbs (as opposed to a grand canonical) ensemble. Moderate disorder tends to drive the system towards stronger hybridization and a standard thermal ensemble, where the approximate conservation law is violated. This behavior is cut off by strong disorder which obstructs many-body effects thus violating ETH and reducing the entanglement entropy.

The inertial mass of a skyrmion arising from spin-phonon interaction is computed exactly within a toy model of the magnetoelastic coupling in a ferromagnetic film. The mass scales as the square of the strength of the magnetoelastic coupling, as the square of the film thickness, and as the first power of the lateral size of the skyrmion. For nanometer skyrmions it is in the ballpark of a few electron masses but may be significantly greater in materials with large magnetostriction. These findings are expected to stand for any complex structure of spin-phonon interaction in real materials. They must be taken into account when addressing the speed of information processing based upon skyrmions.

We study the scrambling of quantum information in local random unitary circuits by focusing on the tripartite information proposed by Hosur et al. We provide exact results for the averaged Rényi-2 tripartite information in two cases: (i) the local gates are Haar random and (ii) the local gates are dual-unitary and randomly sampled from a single-site Haar-invariant measure. We show that the latter case defines a one-parameter family of circuits, and prove that for a “maximally chaotic” subset of this family quantum information is scrambled faster than in the Haar-random case. Our approach is based on a standard mapping onto an averaged folded tensor network, that can be studied by means of appropriate recurrence relations. By means of the same method, we also revisit the computation of out-of-time-ordered correlation functions, rederiving known formulas for Haar-random unitary circuits, and presenting an exact result for maximally chaotic random dual-unitary gates.

Cubic double perovskites that host heavy ions with total angular momentum $J$ = 2 can exhibit a singular magnetic state epitomized by a lone octupole and bulk ferro-type magnetism. It exists in the Chen-Balents Hamiltonian with a quadrupole interaction and competing exchange forces between the ions. Our symmetry inspired analysis mirrors the Dzyaloshinskii-Man'ko theory of latent antiferromagnetic ordering, and a 3k collinear structure. Experimental tests for the singular state include neutron or resonant x-ray Bragg diffraction.

We theoretically propose a mechanism for the anomalous Hall effect (AHE) in an antiferromagnetic (AFM) state of $\kappa$-type organic conductors. We incorporate the spin-orbit coupling in the effective Hubbard model on the $\kappa$-type lattice structure, taking into account the orientation of the molecules and their arrangement with dimerization. Treating this model by means of the Hartree-Fock approximation and the linear response theory, we find that an intrinsic contribution to the Hall conductivity becomes nonzero in the electron-doped AFM metallic phase with a small canted ferromagnetic moment. We show that, contrary to the conventional wisdom, the spin canting is irrelevant to the Hall response; the nonzero Hall conductivity originates from the collinear component of the AFM order in the presence of the spin-orbit coupling. These features are well explained analytically in the limit of strong dimerization on the anisotropic triangular lattice. Furthermore, we present an intuitive picture for the present AHE by considering the real-space configuration of emergent magnetic fluxes. We also find that the Hall response appears even in the undoped AFM insulating phase at nonzero frequency as the magneto-optical Kerr effect, which is enhanced around the charge-transfer excitations. We discuss possible detections of the AHE in ET based compounds.

Here, we present an analysis of the mobility-limiting mechanisms of a two-dimensional hole gas on hydrogen-terminated diamond surfaces. The scattering rates of surface impurities, surface roughness, nonpolar optical phonons, and acoustic phonons are included. Using a Schrödinger/Poisson solver, the heavy-hole, light-hole, and split-off bands are treated separately. To compare the calculations with experimental data, Hall-effect devices were fabricated and measured at temperatures ranging from 25 to 700 K with hole sheet densities ranging from 2 to $6\times {10}^{12}{\mathrm{cm}}^{-2}$ and typical mobilities measured from 60 to $100{\mathrm{cm}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$ at room temperature. Existing data from literature were also used, which span sheet densities above $1\times {10}^{13}{\mathrm{cm}}^{-2}$. Our analysis indicates that, for low sheet densities, surface impurity scattering by charged acceptors and surface roughness are not sufficient to account for the low mobility. Moreover, the experimental data suggest that long-range potential fluctuations exist at the diamond surface and are, particularly, enhanced at lower sheet densities. Thus, a second type of surface impurity scattering is proposed and is presumed to arise by disorder related to the carbon-hydrogen dipoles.

The quantum Hall effect (QHE) is broadly studied in the films of semiconductors, conductors, topological insulators, and topological semimetals. Wedge-shaped samples, guaranteeing the uniform properties of materials, bring obscure characteristics connected to the sample geometry. Here we study the QHE in wedge-shaped samples by using a simple electron gas model. We find that the Hall resistance shows anomalous behaviors: the Hall plateau value shifts when measuring from different lateral terminals, the Hall resistances in positive and negative magnetic fields are not equal, and the Hall resistance depends on the direction of the tilted magnetic field. In addition, the longitudinal resistance also has anomalous characteristics in wedge-shaped samples. These results are very similar to the QHE based on the Weyl orbits observed in a recent experiment, although they are different in origin. These anomalous behaviors in the trivial wedge-shaped sample originate from the spatial redistribution of Landau levels; that is, the edge state can follow an equal-thickness path in the bulk.

Spin-phonon interactions are one of the mechanisms limiting the lifetime of spin qubits made in semiconductor quantum dots. At variance with other mechanisms such as charge noise, phonons are intrinsic to the device and can hardly be mitigated. They set, therefore, fundamental limits to the relaxation time of the qubits. Here we introduce a general framework for the calculation of the spin (and charge) transition rates induced by bulk (3D) and strongly confined 1D or 2D phonons. We discuss the particular case of hole spin-orbit qubits described by the six bands $\mathit{k}·\mathit{p}$ model. We next apply this theory to a hole qubit in a silicon-on-insulator device. We show that spin relaxation in this device is dominated by a band mixing term that couples the holes to transverse acoustic phonons through the valence band deformation potential $d$, and we optimize the bias point and magnetic field orientation to maximize the number of Rabi oscillations $Q$ that can be achieved within relaxation time $T_1$. Despite the strong spin-orbit coupling in the valence band, the phonon-limited $Q$ can reach a few tens of thousands. We next explore the effects of phonon confinement in 1D and 2D structures and the impact of the encapsulation materials on the relaxation rates. We show that the spin lifetimes can depend on the structure of the device over micrometer-long length scales and that they improve when the materials around the qubit get harder. Phonon engineering in semiconductor qubits may therefore become relevant once the extrinsic sources of relaxation have been reduced.

Arrangement of interacting particles on a sphere is historically a well-known problem, however, ordering of particles with anisotropic interaction, such as the dipole-dipole interaction, has remained unexplored. We calculate the equilibrium orientational ordering of point dipoles on a sphere with fixed positional order with numerical minimization of interaction energy and analyze stable configurations depending on their symmetries and degrees of ordering. We find that a macrovortex is a generic ground state for locally triangular spherical lattices with various discrete rotational symmetries for different system sizes, whereas higher-energy metastable states are similar but less ordered. We observe orientational phase transitions and hysteresis in response to changing external field both for the fixed sphere orientation with respect to the field as well as for a freely rotating sphere. For the case of a freely rotating sphere, we also observe changes in the symmetry axis with increasing field strength.

We developed a Landau-type theory for the description of polar phenomena in low-dimensional transition metal dichalcogenides (TMDs), specifically exploring the flexoelectric origin of the polarization induced by a spontaneous bending and by inversion symmetry breaking due to the interactions with substrate. We consider the appearance of the spontaneous out-of-plane polarization due to the flexoelectric coupling with the strain gradient of the spontaneous surface rippling and surface-induced piezoelectricity. Performed calculations proved that the out-of-plane spontaneous polarization, originating from the flexoelectric effect in a rippled TMD, is bistable and reversible by a nonuniform electric field. In contrast, the spontaneous polarization induced by a misfit strain and symmetry-sensitive surface-induced piezoelectric coupling, cannot be reversed by an external electric field. Special attention is paid to the spectral analysis of the linear dielectric susceptibility and gain factor, which enhancement is critically important for the observation of the polar phenomena in low-dimensional TMDs by the surface-enhanced vibrational spectroscopy.