The spin wave stiffness was measured by small-angle neutron scattering method in the Dzyaloshinskii-Moriya helimagnet compounds ${\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x\mathrm{Si}$ with $x=0.25,0.30,0.50$. It has been shown that the spin wave dispersion in the fully polarized state is anisotropic due to Dzyaloshinskii-Moriya interaction. It is reflected in the neutron scattering pattern as two circles for neutrons obtaining and losing the magnon energy, respectively. The centers of the circles are shifted by the momentum transfer oriented along the applied magnetic field $\mathbf{H}$ and equal to the wave vector of the spiral $\pm {\mathbf{k}}_s$. The radius of the circles is directly related to the stiffness of spin waves and depends on the magnetic field. We have found that the spin-wave stiffness $A$ change weakly with temperature for each individual compound. On the other hand, the spin-wave stiffness $A$ increases linearly with $x$ in contrast to the $x$ dependences of the critical temperature $T_c$ and the low-temperature ordered moment. Experimentally obtained values of the stiffness $A$ approve quantitative applicability of the Bak-Jensen model for the compounds under study.

We present a detailed study of photonic heat transport across a Josephson junction coupled to two arbitrary linear circuits having different temperatures. First, we consider the linear approximation, in which a nonlinear Josephson potential is replaced by a quadratic one and the junction acts as an inductor. Afterwards, we discuss the effects of junction anharmonicity. We separately consider the weak-coupling limit, in which the Bloch band structure of the junction energy spectrum plays an important role, and the opposite strong-coupling regime. We apply our general results to two specific models: a Josephson junction coupled to two Ohmic resistors and two resonators. We derive simple analytical approximations for the photonic heat flux in many limiting cases. We demonstrate that electric circuits with embedded Josephson junctions provide a useful platform for quantum thermodynamics experiments.

The in-plane orientation of the magnetization in the center of domain walls is measured in Co/Ir(111) as a function of Co thickness via scanning electron microscopy with polarization analysis. Uncapped, thermally evaporated cobalt on an Ir(111) single-crystal surface is imaged in situ in ultrahigh vacuum. The initial pseudomorphic growth with an atomically flat interface of cobalt on iridium ensures comparability to theoretical calculations and provides a study of an interface that is as ideal as possible. Below a cobalt thickness of 8.8 monolayers, the magnetic domain walls are purely Néel oriented and show a clockwise sense of rotation. For larger thicknesses the plane of rotation changes and the domain walls show a significant Bloch-like contribution, allowing one to calculate the strength of the Dzyaloshinskii-Moriya interaction (DMI) from energy minimization. From the angle between the plane of rotation and the domain-wall normal an interfacial DMI parameter $D_{\mathrm{s}}=-\left(1.07\pm 0.05\right)\mathrm{pJ}/\mathrm{m}$ is determined, which corresponds to a DMI energy per bond between two Co atoms at the interface of $d_{\mathrm{tot}}=-\left(1.04\pm 0.05\right)\mathrm{meV}$.

A local optimization method based on Bayesian Gaussian processes is developed and applied to atomic structures. The method is applied to a variety of systems including molecules, clusters, bulk materials, and molecules at surfaces. The approach is seen to compare favorably to standard optimization algorithms like the conjugate gradient or Broyden-Fletcher-Goldfarb-Shanno in all cases. The method relies on prediction of surrogate potential energy surfaces, which are fast to optimize, and which are gradually improved as the calculation proceeds. The method includes a few hyperparameters, the optimization of which may lead to further improvements of the computational speed.

Using Fourier-transform infrared spectroscopy and optical ellipsometry, room temperature spectra of complex conductivity of single crystals of hexaborides ${\mathrm{Gd}}_x{\mathrm{La}}_{1-x}{\mathrm{B}}_6,x\left(\text{Gd}\right)=\text{0},0.01,0.1,0.78,1$, are determined in the frequency range $30–35000{\text{cm}}^{-1}$. In all compounds, in addition to the Drude free-carrier spectral component, broad excitations are discovered with unusually large dielectric contributions $\mathrm{\Delta }\varepsilon =7000–15000$ and non-Lorentzian line shapes. It is suggested that the origin of the excitations is connected with the dynamic cooperative Jahn-Teller effect of ${\mathrm{B}}_6$ clusters. Analysis of the spectra together with the results of dc and Hall resistivity measurements show that only $25–50\%$ of the conduction band electrons are contributing to the free carrier ac conductivity, with the rest being involved in the formation of an overdamped excitation, thus providing a possible explanation, in terms of nonequilibrium (hot) electrons in these hexaborides, of both the remarkably low work function of thermoemission of ${\mathrm{Gd}}_x{\mathrm{La}}_{1-x}{\mathrm{B}}_6$ and the non-Fermi-liquid behavior in ${\mathrm{GdB}}_6$ crystals.

A lack of space-inversion symmetry along with broken time-reversal symmetry at ferromagnetic/ferroelectric interfaces gives rise to the electric field control of the effective magnetic field and the Dzyaloshinskii-Moriya interaction, thus allowing for the formation of multiferroic skyrmions at room temperature. The electric-field-driven evolution of spin textures at the ferromagnetic/ferroelectric interface is investigated by means of Monte Carlo simulations. It is demonstrated that the skyrmion lattice can be stabilized by the moderate interfacial magnetoelectric couplings. The chirality, radius, position, and numbers of skyrmions are found to be tunable by an external the electric field. The nonequilibrium dynamics of skyrmions, however, strongly depends on the frequency of the applied time-oscillating electric field. With the increase of the frequency of the ac electric field, multiferroic skyrmions become unstable and after several periods they are, ultimately, damping down to the helimagnetic phase. Under microwavelike electric fields, the dynamic multiferroic response of the skyrmion lattice is anisotropic and inhomogeneous. The electric-field-induced resonance spectrum of the magnetic skyrmion with a distinct peak in the imaginary part of permeability is successfully simulated by the Fourier transformation of magnetization.

We use a scanning nanometer-scale superconducting quantum interference device (SQUID) to image individual vortices in amorphous superconducting MoSi thin films. Spatially resolved measurements of the magnetic field generated by both vortices and Meissner screening satisfy the Pearl model for vortices in thin films and yield values for the Pearl length and bulk penetration depth at 4.2 K. Flux pinning is observed and quantified through measurements of vortex motion driven by both applied currents and thermal activation. The effects of pinning are also observed in metastable vortex configurations, which form as the applied magnetic field is reduced and magnetic flux is expelled from the film. Understanding and controlling vortex dynamics in amorphous thin films is crucial for optimizing devices such as superconducting nanowire single photon detectors (SNSPDs), the most efficient of which are made from MoSi, WSi, and MoGe.

Proximity-induced superconductivity in three-dimensional (3D) topological insulators forms a new quantum phase of matter and accommodates exotic quasiparticles such as Majorana bound states. One of the biggest drawbacks of the commonly studied 3D topological insulators is the presence of conducting bulk that obscures both surface states and low energy bound states. Introducing superconductivity in topological Kondo insulators such as ${\mathrm{SmB}}_6$, however, is promising due to their true insulating bulk at low temperatures. In this work, we develop an unconventional Josephson junction by coupling superconducting Nb leads to the surface states of a ${\mathrm{SmB}}_6$ crystal. We observe a robust critical current at low temperatures that responds to the application of an out-of-plane magnetic field with significant deviations from usual Fraunhofer patterns. The appearance of Shaphiro steps under microwave radiation gives further evidence of a Josephson effect. Moreover, we explore the effects of Kondo breakdown in our devices, such as ferromagnetism at the surface and anomalous temperature dependence of supercurrent. Particularly, the magnetic diffraction patterns show an anomalous hysteresis with the field sweep direction suggesting the coexistence of magnetism with superconductivity at the ${\mathrm{SmB}}_6$ surface. The experimental work will advance the current understanding of topologically nontrivial superconductors and emergent states associated with such unconventional superconducting phases.

We have imaged the current noise with atomic resolution in a Josephson scanning tunneling microscope with a Pb-Pb junction. By measuring the current noise as a function of applied bias, we reveal the change from single-electron tunneling above the superconducting gap energy to double-electron charge transfer below the gap energy when Andreev processes become dominant. Our spatially resolved noise maps show that this doubling occurs homogeneously on the surface, and also on impurity locations, demonstrating that indeed the charge pairing is not influenced by disruptions in the superconductor smaller than the superconducting coherence length.

We investigate the zero-temperature quantum phases of a quasi-one-dimensional zigzag chain of dipoles that are polarized in a plane by an external electric field. Since the Hamiltonian contains nearest-neighbor and next-nearest-neighbor hopping and interaction terms, this model allows frustration, which induces phases that can be interesting and unusual. By using the density matrix renormalization group algorithm, we produce a complex phase diagram. This is an extension of an earlier work by Wang et al. [Phys. Rev. A 96, 043615 (2017)].

It is an important open problem to understand the landscape of non-Abelian fractional quantum Hall phases which can be obtained starting from physically motivated theories of Abelian composite particles. We show that progress on this problem can be made using recently proposed non-Abelian bosonization dualities in $2+1$ dimensions, which morally relate $U{\left(N\right)}_k$ and $\mathrm{SU}{\left(k\right)}_{-N}$ Chern-Simons-matter theories. The advantage of these dualities is that regions of the phase diagram which may be obscure on one side of the duality can be accessed by condensing local operators on the other side. Starting from parent Abelian states, we use this approach to construct Landau-Ginzburg theories of non-Abelian states through a pairing mechanism. In particular, we obtain the bosonic Read-Rezayi sequence at fillings $\nu =k/(kM+2)$ by starting from $k$ layers of bosons at $\nu =1/2$ with $M$ Abelian fluxes attached. The Read-Rezayi states arise when $k$ clusters of the dual non-Abelian bosons condense. We extend this construction by showing that $N_f$-component generalizations of the Halperin (2,2,1) bosonic states have dual descriptions in terms of $\mathrm{SU}{(N_f+1)}_1$ Chern-Simons-matter theories, revealing an emergent global symmetry in the process. Clustering $k$ layers of these theories yields a non-Abelian $\mathrm{SU}\left(N_f\right)$-singlet state at filling $\nu =k{N}_f/(N_f+1+kM{N}_f)$.

Subsystem symmetry protected topological (SSPT) order is a type of quantum order that is protected by symmetries acting on lower-dimensional subsystems of the entire system. In this paper, we show how SSPT order can be characterized and detected by a constant correction to the entanglement area law, similar to the topological entanglement entropy. Focusing on the paradigmatic two-dimensional cluster phase as an example, we use tensor network methods to give an analytic argument that almost all states in the phase exhibit the same correction to the area law, such that this correction may be used to reliably detect the SSPT order of the cluster phase. Based on this idea, we formulate a numerical method that uses tensor networks to extract this correction from ground-state wave functions. We use this method to study the fate of the SSPT order of the cluster state under various external fields and interactions, and find that the correction persists unless a phase transition is crossed, or the subsystem symmetry is explicitly broken. Surprisingly, these results uncover that the SSPT order of the cluster state persists beyond the cluster phase, thanks to a new type of subsystem time-reversal symmetry. Finally, we discuss the correction to the area law found in three-dimensional cluster states on different lattices, indicating rich behavior for general subsystem symmetries.

We theoretically investigate the magnetic brightening, valley Zeeman splitting, and valley dynamics of long-lived A and B dark excitons (A-DEs and B-DEs) in monolayer ${\mathrm{WS}}_2$, subjected to tilted magnetic fields. Biexciton states and indirect intervalley excitons, with the latter composed of a hole in the $K$ valley and an electron in the $\mathrm{\Lambda }$ valley, are also taken into account. We reveal that both in-plane and out-of-plane field components greatly affect the magnetic brightening process due to correlations among different excitonic quasiparticles but in distinct roles. Specifically, the in-plane component primarily enables the dark-state brightening, while the perpendicular one not only modifies the bright-dark splitting inside a given valley, but also lifts the valley degeneracy of either bright or dark excitonic states. Moreover, in the presence of a tilted magnetic field with a nonzero in-plane component, we observe that both A-DEs and B-DEs can be brightened, with the latter requiring a much stronger field for a certain intensity of light emission. Remarkably, we find that the valley splitting of A-DEs is around twice as large as that of A bright excitons but vanishes for B-DEs, as a result of the combined effect of the spin and orbital magnetic moments on the energy shifts of the two valleys. In addition, as the tilt angle of the field with respect to the normal direction of ${\mathrm{WS}}_2$ sheet increases from $0^{\circ }$ to ${180}^{\circ }$, the bright-dark splittings for A and B excitons exhibit an opposite behavior, but both feature an “X”-like pattern when the field is oriented in-plane. Finally, it is observed that the temperature greatly affects the light emission of bright and brightened dark states, while the corresponding temperature dependence is distinct for A and B excitons.

A scheme is proposed to solve the structure of incommensurate interfaces, starting from high-resolution images of electron microscopy, supplemented by adapted simulation techniques, and complemented by theoretical tools. Direct silicon bonding is a way to produce artificial interfaces, in particular incommensurate ones. We focus on a technology-driven tilt grain boundary in silicon. While the Fibonacci sequence, linked to the golden ratio, is a prototype of the quasicrystalline structures, a silver-ratio sequence allows us to analyze this incommensurate interface. The fourfold coordination of the Si atoms is kept at the interface.

We study a model of a p-n junction in single-layer graphene in the presence of a perpendicular magnetic field and spin-orbit interactions. By solving the relevant quantum-mechanical problem for a potential step, we determine the exact spectrum of spin-resolved dispersive Landau levels. Close to zero energy, we find a pair of linearly dispersing zero modes, which possess a wave-vector-dependent spin polarization and can be regarded as quantum analogs of spinful snake states. We show that the Rashba spin-orbit interaction, in particular, produces a wave vector shift between the dispersions of these modes with observable interference effects. These effects can in principle provide a way to detect the presence of Rashba spin-orbit interaction and measure its strength. Our results suggest that a graphene p-n junction in the presence of strong spin-orbit interaction could be used as a building block in a spin field-effect transistor.

Experiments on rare-earth filled skutterudites demonstrate an intriguing array of thermodynamic, transport, and superconducting properties, and bring to fore theoretical challenges posed by $f$-electron systems. First-principle calculations based density functional theory and its extensions for strongly correlated systems such as the Hubbard $U$ correction, provide valuable information about electronic structure that can be used to understand experiments. We present a comprehensive study of the electronic structure and Fermi surface of a series of rare-earth filled skutterudites, $R{\mathrm{Pt}}_4{\mathrm{Ge}}_{12}$ (where $R$ = La, Ce, Pr), aimed at shedding light on: consequences of progressive increase of $f$-orbital occupancy in the series; the effects of the Hubbard parameter $U$; and the Fermi surfaces, band structures, and densities of states. The calculated Fermi surfaces may be relevant to the question of multiband versus single-band superconductivity. Computed densities of states qualitatively explain the available resonant photoemission spectroscopy experiments, and (together with available specific heat measurements) provide estimates of the effective masses. We also show the existence of pseudogaps in the total density of states which may be relevant for the thermoelectric properties of these systems.

We theoretically investigate the fluorine doping in $\mathrm{LaOBi}{\mathrm{S}}_2$-type quaternary compounds ($\mathrm{LaOBi}{\mathrm{S}}_2$, $\mathrm{NdOBi}{\mathrm{S}}_2$, $\mathrm{LaOBiS}{\mathrm{e}}_2$, and $\mathrm{LaOSbS}{\mathrm{e}}_2$), which are promising candidates for thermoelectric and superconducting materials. These compounds possess a layered structure comprising blocking LnO ($Ln=\mathrm{La}$, Nd, etc.) layers and conducting $PnC{h}_2$ ($Pn=\mathrm{Bi}$, Sb; $Ch=\mathrm{S}$, Se) layers. Their carrier concentration is generally tuned via substitutional doping of F atoms in the O site for improving the thermoelectric performance or the superconductivity; however, the tunability of the electrical properties via F doping strongly depends on constituent elements. In order to elucidate the difference, we theoretically examine the electronic and structural properties of these F-doped systems using first-principles calculation. Our results show that the monoclinic distortion of the mother compound, which is closely related to the Pn element, can drastically decrease the capability of F doping. Replacement of the Ln atom from La to Nd in $Ln\mathrm{OBi}{\mathrm{S}}_2$ makes F doping difficult, which is consistent with experimental observation. We also find that the tetragonal structure is gradually stabilized by F doping for all the systems investigated in this study. Our results will be important knowledge for controlling the electrical properties of $\mathrm{LaOBi}{\mathrm{S}}_2$-type compounds both as thermoelectric and superconducting materials.

The dynamical-gap formation in an anisotropic tilted Dirac semimetal modulated by intense elliptically polarized light is addressed through the solution of the time-dependent Schrödinger equation for the two-dimensional Dirac Hamiltonian via the Floquet theorem. The time-dependent wave functions and the quasienergy spectrum of the two-dimensional Dirac Hamiltonian under normal incidence of elliptically polarized electromagnetic waves are obtained using a nonperturbative approach. In it, the Schrödinger equation is reduced to an ordinary second-order differential Mathieu equation. It is shown that the stability conditions of the Mathieu functions are directly inherited by the wave function resulting in a quasiparticle spectrum consisting of bands and gaps determined by dynamical diffraction and resonance conditions between the electron and the electromagnetic wave. Estimations of the electromagnetic field intensity and frequency, as well as the magnitude of the generated gap, are obtained for the $8\text{−}Pmmn$ phase of borophene. We provide a simple method that enables us to predict the formation of dynamical gaps of unstable wave functions and their magnitudes. This method can readily be adapted to other anisotropic tilted Dirac semimetals.