We theoretically study quantum transport through a quantum dot coupled to Majorana bound states confined at the ends of a topological superconducting nanowire. The topological superconductor forms a loop and is threaded by a tunable magnetic flux, which allows one to control the electron transport in the system. In particular, we investigate phonon-assisted transport properties in the device when the central quantum dot interacts with a single long-wave optical phonon mode. We find that when the two Majorana bound states are unhybridized, the zero-temperature linear conductance has a $2\pi$ periodicity as a function of magnetic flux phase, independent of the electron-phonon interaction, the quantum dot energy, or the finite values of dot-Majorana couplings. For a finite overlap between the Majorana bound states, the linear conductance periodicity generally changes to $4\pi$ either due to a finite electron-phonon coupling strength, or a dot energy level that is tuned away from the Fermi level. Additionally, the differential conductance periodicity changes from $2\pi$ to $4\pi$ when the Majorana bound states hybridize and the electron-phonon coupling is finite. Our results provide insight into transport signatures expected in topological quantum computational platforms that integrate quantum dots as a means for Majorana qubit readout. The energy exchange with an environmental bath, here a single phonon mode, significantly alters the current signatures expected from Majorana modes.

Solving the many-body Schrödinger equation in continuous spaces with the presence of strong correlations is an extremely important and challenging issue in quantum physics. In this work, we propose the functional tensor network (FTN) approach to solve the many-body Schrödinger equation. Provided the orthonormal functional bases, we represent the coefficients of the many-body wave function as a tensor network. The observables, such as energy, can be calculated simply by tensor contractions. Simulating the ground state becomes solving a minimization problem defined by the tensor network. An efficient gradient-decent algorithm based on automatically differentiable tensors is proposed. We here take the matrix product state (MPS), whose complexity scales only linearly with the system size, as an example. We apply our approach to solve the ground state of coupled harmonic oscillators and achieve high accuracy by comparing our results with the exact solutions. Reliable results are also given in the presence of three-body interactions, where the system cannot be decoupled from isolated oscillators. Our approach is simple and, with well-controlled error, essentially different from highly nonlinear neural-network solvers. Our work extends the applications of the tensor network from quantum lattice models to systems in continuous space. The FTN can be used as a general solver of the differential equations with many variables. The MPS exemplified here can be generalized to, e.g., fermionic tensor networks to solve the electronic Schrödinger equation.

Heterostructuring provides different ways to manipulate the orbital degrees of freedom and to tailor orbital occupations in transition-metal oxides. However, the reliable prediction of these modifications remains a challenge. Here we present a detailed investigation of the relationship between the crystal and electronic structure in ${\mathrm{YVO}}_3\text{−}{\mathrm{LaAlO}}_3$ superlattices by combining ab initio theory, scanning transmission electron microscopy, and x-ray diffraction. Density functional theory simulations including an on-site Coulomb repulsion term accurately predict the crystal structure and, in conjunction with x-ray diffraction, provide an explanation for the lifting of degeneracy of the vanadium $d_{xz}$ and $d_{yz}$ orbitals that was recently observed in this system. In addition, we unravel the combined effects of electronic confinement and octahedral connectivity by disentangling their impact from that of epitaxial strain. Our results demonstrate that the specific orientation of the substrate and the thickness of the ${\mathrm{YVO}}_3$ slabs in the multilayer can be utilized to reliably engineer orbital polarization.

Parafermionic zero modes are non-Abelian excitations which have been predicted to emerge at the boundary of topological phases of matter. Contrary to earlier proposals, here we show that such zero modes may also exist in multilegged star junctions of quantum Hall states. We demonstrate that the quantum states spanning the degenerate parafermionic Hilbert space may be detected and manipulated through protocols employing quantum antidots and fractional edge modes. Such star-shaped setups may be the building blocks of two-dimensional parafermionic networks.

We study the structure-stability relationship of Lennard-Jones (LJ) clusters from a point of view of vibrations. By assuming the size up to $N=1610$, we demonstrate that the $N$ dependence of the maximum vibrational frequency reflects the geometry of the core (the interior of a cluster) that will determine the overall geometry of the cluster. This allows us to identify the formation of nonicosahedral structures for $N\le 150$, the vacancy formation at the core for $N\ge 752$, and the transition from icosahedral to decahedral structures at $N=1034$. We apply the maximum frequency analysis to classify metastable clusters for $19\le N\le 39$, where transformation pathways between different structures are visualized, and the energy barrier height is estimated simultaneously.

Due to the long electrical screening length of an insulator, changes in local ferroelectric (FE) polarization can cause significant electrostatic potential drops or rises across the whole insulating region, which can be designed to enhance the tunneling electroresistance (TER) effect. First-principles calculations of ${\mathrm{Co}}_2\mathrm{MnSi}/{\mathrm{BaTiO}}_3/{\mathrm{SrRuO}}_3$ multiferroic tunnel junctions predict a unique local FE polarization at the MnSi-${\mathrm{TiO}}_2$ interface, which is giant (tiny) in the right-polarized (left-polarized) state. For the right-polarized state, the large interfacial FE polarization greatly lowers the FE barrier height, making it close to zero. However, for the left-polarized state, because its band edges near the MnSi-${\mathrm{TiO}}_2$ interface are usually below the Fermi level, the tiny interfacial FE polarization has a weak effect on the electrostatic potential, maintaining a sizable barrier height. This FE-controlled barrier height produces an optimistic TER ratio of up to $1.1\times {10}^3$. Even if the large interface polarization is unexpectedly fixed, the TER ratio remains ultrahigh, increasing the fault tolerance of the interface-enhanced TER effect in applications.

The experiment shows that hydrogenated ${\mathrm{U}}_2{\left({\mathrm{Ni}}_{1-x}{\mathrm{Fe}}_x\right)}_2\mathrm{Sn}$ is antiferromagnetic for $x=0$. With increasing Fe content, the Néel temperature decreases and tends to 0 K at $x\sim 20\%$. Further increase of $x$ results in the ferromagnetism of the system. This paper suggests an explanation why the material that, from its chemical composition, is intermediate between antiferromagnet ${\mathrm{U}}_2{\mathrm{Ni}}_2\mathrm{Sn}$ and Pauli paramagnet ${\mathrm{U}}_2{\mathrm{Fe}}_2\mathrm{Sn}$ turns in the hydrogenated form to the ferromagnetic state—a state that is very unusual for the U compounds with the given crystal lattice. Our theoretical study is based on density functional theory (DFT) and $\mathrm{DFT}+U$ calculations. It begins with the calculation of ${\mathrm{U}}_2{\mathrm{Ni}}_2\mathrm{Sn}$ and ${\mathrm{U}}_2{\mathrm{Fe}}_2\mathrm{Sn}$ in their experimental lattices. Next, we show that for the lattice parameters of ${\mathrm{U}}_2{\mathrm{Ni}}_2\mathrm{Sn}, {\mathrm{U}}_2{\mathrm{Fe}}_2\mathrm{Sn}$ becomes magnetic. To understand deeper the dependence of the magnetic states on the lattice parameters, we model quantum phase transitions in both parent systems. We find that a drastic difference of the $3d-5f$ hybridization in the two systems leads to fundamentally different types of the magnetic states. ${\mathrm{U}}_2{\mathrm{Ni}}_2\mathrm{Sn}$ has well-defined U atomic moments and can be mapped on the Heisenberg-type Hamiltonian of interacting U moments. In ${\mathrm{U}}_2{\mathrm{Fe}}_2\mathrm{Sn}$, strong $5f-3d$ hybridization leads to both the Pauli paramagnetism for the equilibrium lattice and the simultaneous appearance of comparable in value U and Fe spin moments for larger lattice parameters. The presence of the Fe moments is shown to be essential for the magnetism of ${\mathrm{U}}_2{\mathrm{Fe}}_2\mathrm{Sn}$, which imposes strong constraint on the magnetic structure of the U sublattice requesting it to be ferromagnetic. The established correlation between U and Fe spin moments is crucial for the explanation of the ferromagnetism of the hydrogenated ${\mathrm{U}}_2{\left({\mathrm{Ni}}_{1-x}{\mathrm{Fe}}_x\right)}_2\mathrm{Sn}$.

The superconducting transition temperature, $T_{\mathrm{c}}$, of FeSe can be significantly enhanced several-fold by applying pressure, electron doping, intercalating spacing layer, and reducing dimensionality. Various ordered electronic phases, such as nematicity and spin density waves, have also been observed accompanying high-$T_{\mathrm{c}}$ superconductivity. In this paper, we have found a series of discrete superconducting phases, with a maximum $T_{\mathrm{c}}$ up to 44 K, in ${\mathrm{H}}^{+}$-intercalated FeSe single crystals using an ionic liquid gating method. Accompanied with the increase of $T_{\mathrm{c}}$, suppression of the nematic phase and evolution from non-Fermi-liquid to Fermi-liquid behavior was observed. An abrupt change in the Fermi surface topology was proposed to explain the discrete superconducting phases. A band structure that favors the high-$T_{\mathrm{c}}$ superconducting phase was also revealed.

We report the magnetic structure and anisotropy of the quasi-one-dimensional $S=\frac{1}{2}$ antiferromagnet ${\mathrm{Na}}_2{\mathrm{CuSO}}_4{\mathrm{Cl}}_2$ obtained by single-crystal neutron scattering, electron spin resonance (ESR), and magnetization measurements, following an earlier study of its dynamics [M. Fujihala et al., Phys. Rev. B 101, 024410 (2020)]. A Néel-type spin structure is formed within the chain of this compound, where the spins point along the $b$ axis, and ESR data indicate an antisymmetric exchange with a uniform Dzyaloshinskii-Moriya (DM) vector pointing along the $b$ axis. The anisotropy $g$ factor and magnetic structure are strong indicators of magnetic anisotropy originating from a symmetric anisotropic exchange interaction and/or a magnetic dipole interaction. These results suggest that these terms of the anisotropic spin Hamiltonian counteract the effect of the DM interaction and stabilize the Néel-type structure in ${\mathrm{Na}}_2{\mathrm{CuSO}}_4{\mathrm{Cl}}_2$.

The structural and magnetic properties of the room-temperature multiferroic bulk $\alpha \text{−}{\mathrm{BiFeO}}_3$ are described by using the magnetic superspace group formalism. The antiferromagnetic cycloid with its propagation vector along the hexagonal [1,1,0] direction cannot be described with trigonal magnetic superspace groups derived from $R3c$. This disagreement shows the necessity to replace trigonal symmetry with monoclinic symmetry. Several phenomena observed experimentally in bulk $\alpha \text{−}{\mathrm{BiFeO}}_3$, e.g., antiferromagnetic cycloid, weak ferromagnetic spin-density wave, and hkl-dependent Bragg peaks' broadening can all be described by using the monoclinic magnetic superspace groups $Cc\left(0\beta 0\right)0$ for clockwise magnetic moments rotation and $C{c}^{\prime }\left(0\beta 0\right)0$ for counterclockwise magnetic moments rotation. The proposed monoclinic superspace groups can also describe anharmonic magnetic modulations, charge modulations, atomic position modulations, as well as weak nonmodulated ferromagnetic ordering or ferroelectric polarization in bulk $\alpha \text{−}{\mathrm{BiFeO}}_3$.

A magnetic impurity on a superconducting substrate induces in-gap Yu-Shiba-Rusinov (YSR) bound states, whose intricate spatial structure crucially influences the possibilities of engineering collective impurity states. By means of a saddle-point approximation, we study the scattering processes giving rise to YSR states in gapped, two-dimensional superconductors. Further, we develop a theory, which relates through a simple analytical expression, an arbitrary energy dispersion of normal electrons in a two-dimensional host to the spatial features of the YSR states. Namely, we find that flatter segments of the Fermi surface with large Fermi velocity enhance the local density of states (LDOS) around the impurity. Our analytical approximation is quantitatively accurate against tight-binding calculations on various lattices with different Fermi surfaces, and it allows to predict the shape and orientation of YSR states observed in scanning tunneling spectroscopy experiments. We illustrate our results with a model of ${\mathrm{NbSe}}_2$.

A theoretical model of transmission and reflection of an electron with spin is proposed for a mesoscopic ring with rotating localized magnetic moment. This model may be realized in a pair of domain walls connecting two ferromagnetic domains with opposite magnetization. If the localized magnetic moment and the traveling spin is ferromagnetically coupled and if the localized moment rotates with opposite chirality in the double path, our system is formulated in the model of an emergent spin-orbit interaction in a ring. The scattering problem for the transmission spectrum of the traveling spin is solved both in a single-path and a double-path model. In the double path, the quantum-path interference changes dramatically the transmission spectrum due to the effect of the Berry phase. Specifically, the spin-flip transmission and reflection are both strictly forbidden.

A path-integral (Lagrangian) formalism is used to derive the effective equations of motion of the anomalous Hall effect with Berry's phase on the basis of the adiabatic condition $|E_{n\pm 1}-E_n|\gg 2\pi \hslash /T$, where $T$ is the typical timescale of the slower system and $E_n$ is the energy level of the fast system. In the conventional definition of the adiabatic condition with $T\to \mathrm{large}$ and fixed energy eigenvalues, no commutation relations are defined for slower variables by the Bjorken-Johnson-Low prescription except for the starting canonical commutators. On the other hand, in a singular limit $|E_{n\pm 1}-E_n|\to \infty$ with specific $E_n$ kept fixed for which any motions of the slower variables $X_k$ can be treated to be adiabatic, the noncanonical dynamical system with deformed commutators and the Nernst effect appears. In the Born-Oppenheimer approximation based on the canonical commutation relations, the equations of motion of the anomalous Hall effect are obtained if one uses an auxiliary variable $X_k^{\left(n\right)}=X_k+{\mathcal{A}}_k^{\left(n\right)}$ with Berry's connection ${\mathcal{A}}_k^{\left(n\right)}$ in the absence of the electromagnetic vector potential $e{A}_k\left(X\right)$ and thus without the Nernst effect. It is shown that the gauge symmetries associated with Berry's connection and the electromagnetic vector potential $e{A}_k\left(X\right)$ are incompatible in the canonical Hamiltonian formalism. The appearance of the noncanonical dynamical system with the Nernst effect is a consequence of the deformation of the quantum principle to incorporate the two incompatible gauge symmetries.

We study topological insulators based on InAs/GaSb/InAs trilayer quantum wells with different InAs thicknesses ranging from 8.0 to 13.5 nm to experimentally ascertain the phase diagram in this material system. Gate-voltage and temperature-dependent transport measurements reveal distinct transport signatures between samples designed from the trivial-insulating, the topological-insulating, up to the semimetallic phase. Two-carrier transport together with pronounced Van Hove singularities are observable only for the samples grown in the topological-insulating phase and if camelback-like dispersions are present in the hybridized valence or conduction band. The different shaping and the amount of Van Hove singularities in our samples deliver information about a turning point inside the topological-insulating phase. Temperature-dependent measurements allow to further confirm the gap energy values for the trivial- and topological-insulating samples. Furthermore, the indirect inverted gaps are found to be more temperature insensitive in comparison to the trivial gap.

Heat capacity of the nuclear-spin system (NSS) in GaAs-based microstructures has been shown to be much greater than expected from dipolar coupling between nuclei, thus limiting the efficiency of NSS cooling by adiabatic demagnetization. It was suggested that quadrupole interaction induced by some small residual strain could provide this additional reservoir for the heat storage. We check and validate this hypothesis by combining nuclear-spin relaxation measurements with adiabatic remagnetization and nuclear magnetic resonance experiments, using electron spin-noise spectroscopy as a unique tool for detection of nuclear magnetization. Our results confirm and quantify the role of the quadrupole splitting in the heat storage within NSS and provide additional insight into the fundamental, but still actively debated relation between a mechanical strain and the resulting electric field gradients in GaAs.

Two-dimensional Dirac materials with a flat band have been demonstrated to possess a plethora of unusual electronic properties, but the optical properties of these materials are less studied. Utilizing $\alpha \text{−}{\mathcal{T}}_3$ lattice as a prototypical system, where $0\le \alpha \le 1$ is a tunable parameter and a flat band through the conic intersection of two Dirac cones arises for $\alpha >0$, we investigate the conductivity of flat-band Dirac material systems analytically and numerically. Motivated by the fact that the imaginary part of the optical conductivity can have significant effects on the optical response and is an important factor of consideration for developing $\alpha \text{−}{\mathcal{T}}_3$ lattice based optical devices, we are led to derive a complete conductivity formula with both the real and imaginary parts. Scrutinizing the formula, we uncover two phenomena. First, for the value of $\alpha$ in some range, two types of optical transitions coexist: one between the two Dirac cones and another from the flat band to a cone, which generate multifrequency transverse electrical propagating waves. Second, for $\alpha =1$ so the quasiparticles become pseudospin-1, the flat-to-cone transition can result in resonant scattering. These results pave the way to exploiting $\alpha \text{−}{T}_3$ lattice for optical device applications in the terahertz-frequency domain.

We propose a three-step periodic drive protocol to engineer two-dimensional (2D) Floquet quadrupole superconductors and three-dimensional (3D) Floquet octupole superconductors hosting zero-dimensional Majorana corner modes (MCMs), based on unconventional $d$-wave superconductivity. Remarkably, the driven system conceives four phases with only zero MCMs, no MCMs, only anomalous $\pi$ MCMs, and both regular zero and anomalous $\pi$ MCMs. To circumvent the subtle issue of characterizing zero and $\pi$ MCMs separately, we employ the periodized evolution operator to architect the dynamical invariants, namely quadrupole and octupole motion in 2D and 3D, respectively, that can distinguish different higher-order topological phases unambiguously. Our study paves the way for the realization of dynamical quadrupolar and octupolar topological superconductors.