The Kondo semiconductors $\mathrm{Ce}{T}_2\mathrm{A}{\mathrm{l}}_{10}$ ($T=\mathrm{Ru}$ and Os) exhibit antiferromagnetic (AFM) orders at unexpectedly high temperatures $T_{\mathrm{N}}=27.0$ and 28.5 K, respectively, whose mechanism remains in debate. We report the break-junction experiments on $4f/5d$-hole and $5d$-electron doped $\mathrm{CeO}{\mathrm{s}}_2\mathrm{A}{\mathrm{l}}_{10}$ as well as nondoped $\mathrm{CeR}{\mathrm{u}}_2\mathrm{A}{\mathrm{l}}_{10}$. The differential conductance spectra $dI/dV$ for $T=\mathrm{Os}$ and Ru show three gap structures; two hybridization gaps $V_1, V_2$ and an AFM gap $V_{\mathrm{AF}}$, whose magnitudes for $T=\mathrm{Os}$ are $15-50\%$ larger than for $T=\mathrm{Ru}$. Doping of $4f/5d$ holes and $5d$ electrons in $\mathrm{CeO}{\mathrm{s}}_2\mathrm{A}{\mathrm{l}}_{10}$ changes the $dI/dV$ spectrum in very different ways. Nevertheless, in all cases, the suppression of $V_1$ is well correlated with those of $V_{\mathrm{AF}}$ and $T_{\mathrm{N}}$. Furthermore, the zero-bias conductance decreases on cooling below $T^{*}$ ($>T_{\mathrm{N}}$) only in the doping region where $V_1$ and $V_{\mathrm{AF}}$ coexist. This fact indicates that the unusual AFM order is preceded by the decrease in the density of states in the presence of $V_1$.

We have used high-resolution transmission spectroscopy to study the exciton level spectrum in ${\mathrm{Cu}}_2\mathrm{O}$ subject to a longitudinal external electric field, i.e., in the geometry where the transmitted light is propagating along the field direction. Different experimental configurations given by the field orientation relative to the crystal and the light polarization have been explored. We focus on the range of small principal quantum numbers $n\le 7$. The number of exciton states belonging to a particular principal quantum number increases with $n$, leading to an enhanced complexity of the spectra. Still, in particular, for $n=3,...,5$, a spectral separation of the different lines is feasible and identification as well as assignment of the dominant state character are possible. We find a strong dependence of the spectra on the chosen light propagation direction and polarization configuration, reflecting the inadequacy of the hydrogen model for describing the excitons. With increasing the field excitonic states with different parity become mixed, leading to optical activation of states that are dark in zero field. As compared with atoms, due to the reduced Rydberg energy states with different $n$ can be brought into resonance in the accessible electric field strength range. When this occurs, we observe mostly crossing of levels within the experimental accuracy showing that the electron and hole motion remains regular. The observed features are well described by detailed calculations accounting for the spin-orbit coupling, the cubic anisotropy effects, and the symmetry-imposed optical selection rules.

HgTe-based quantum wells (QWs) possess very strong spin-orbit interaction (SOI) and have become an ideal platform for the study of fundamental SOI-dependent phenomena and the topological insulator phase. Circular photogalvanic effect (CPGE) in HgTe QWs is of great interest because it provides an effective optical access to probe the spin-related information of HgTe systems. However, the complex band structure and large spin splitting of HgTe QWs makes it inadequate to analyze the experimental results of CPGE in HgTe QWs [B. Wittmann et al., Semicond. Sci. Technol. 25, 095005 (2010)] with reduced band models. Here, based on the realistic eight-band $\mathbf{k}·\mathbf{p}$ Hamiltonian and combined with the density-matrix formalism, we present a detailed theoretical investigation of CPGE in (001)-oriented ${\mathrm{Hg}}_{0.3}{\mathrm{Cd}}_{0.7}\mathrm{Te}/\mathrm{HgTe}/{\mathrm{Hg}}_{0.3}{\mathrm{Cd}}_{0.7}\mathrm{Te}$ QWs. We find the CPGE currents in HgTe QWs in the heavily inverted regime are significantly enhanced due to the strong distortion of band dispersion at a certain range of the energy spectrum. This enhancement effect could offer an experimental certificate that the HgTe QW is in the heavily inverted phase (usually accompanied with the emergence of two-dimensional topological edge states), and could also be utilized in engineering the high efficiency ellipticity detector of infrared and terahertz radiation [S. N. Danilov et al., J. Appl. Phys. 105, 013106 (2009)]. Additionally, within the same theoretical framework, we also investigate the interplay effect of structure inversion asymmetry and bulk inversion asymmetry and the pure spin currents driven by linearly polarized light in HgTe QWs.

The optical properties of dielectric plates coated with gapped graphene are investigated on the basis of first principles of quantum electrodynamics. The reflection coefficients and reflectivities of graphene-coated plates are expressed in terms of the polarization tensor of gapped graphene and the dielectric permittivity of plate material. Simple approximate expressions for the required combinations of components of the polarization tensor applicable in the wide frequency region, where the presence of a gap influences the optical properties, are found. Numerical computations of the reflectivities of graphene-coated $\mathrm{SiO}{}_2$ plates are performed for different values of the mass-gap parameter at different temperatures. It is shown that with an increasing gap width the reflectivity of a graphene-coated plate at the normal incidence decreases by up to a factor of 8 depending on the values of frequency and mass-gap parameter. The angle dependences of reflectivities for both polarizations of the incident electromagnetic waves have been computed for Si and $\mathrm{SiO}{}_2$ plates coated with gapped graphene. We demonstrate that the TM reflectivity has a minimum value at some angle of incidence depending on the mass-gap parameter, frequency and temperature, whereas the TE reflectivity depends on the angle of incidence monotonously. However, for the graphene coatings with a nonzero mass-gap parameter the reflected light cannot be fully polarized. Possible applications of the obtained results are discussed.

We revisit model calculations of the anomalous Hall effect (AHE) and show that, in isotropic Rashba-coupled two-dimensional electron gas with pointlike potential impurities, the full solution of the semiclassical Boltzmann equation (SBE) may differ from the widely used $1/{\tau }^{\left|\right|}$ and $1/{\tau }^{\perp }$ solution [Schliemann and Loss, Phys. Rev. B 68, 165311 (2003)]. Our approach to solving the SBE is consistent with the integral equation approach [Vyborny et al., Phys. Rev. B 79, 045427 (2009)] but in the present case, we reduce the description to band-index-dependent transport relaxation times. When both Rashba bands are partially occupied, these are determined by solving a system of linear equations. Detailed calculations show that, for intrinsic and hybrid skew scatterings the difference between $1/{\tau }^{\left|\right|}$ and $1/{\tau }^{\perp }$ and the full solution of SBE is notable for large Fermi energies. For coordinate-shift effects, the side-jump velocity acquired in the interband elastic-scattering process is shown to be more important for larger Rashba coupling and may even exceed the intraband one for the outer Rashba band. The coordinate-shift contribution to AHE in the considered case notably differs from that in the limit of smooth disorder potential analyzed before.

We present a boundary integral formulation of electromagnetic scattering by homogeneous bodies that are characterized by linear constitutive equations in the frequency domain. By working with the Cartesian components of the electric $\mathit{E}$ and magnetic $\mathit{H}$ fields and with the scalar functions $(\mathit{r}·\mathit{E})$ and $(\mathit{r}·\mathit{H})$ where $\mathit{r}$ is a position vector, the problem can be cast as having to solve a set of scalar Helmholtz equations for the field components that are coupled by the usual electromagnetic boundary conditions at material boundaries. This facilitates a direct solution for the surface values of $\mathit{E}$ and $\mathit{H}$ rather than having to work with surface currents or surface charge densities as intermediate quantities in existing methods. Consequently, our formulation is free of the well-known numerical instability that occurs in the zero-frequency or long-wavelength limit in traditional surface integral solutions of Maxwell's equations and our numerical results converge uniformly to the static results in the long-wavelength limit. Furthermore, we use a formulation of the scalar Helmholtz equation that is expressed as classically convergent integrals and does not require the evaluation of principal value integrals or any knowledge of the solid angle. Therefore, standard quadrature and higher order surface elements can readily be used to improve numerical precision for the same number of degrees of freedom. In addition, near and far field values can be calculated with equal precision, and multiscale problems in which the scatterers possess characteristic length scales that are both large and small relative to the wavelength can be easily accommodated. From this we obtain results for the scattering and transmission of electromagnetic waves at dielectric boundaries that are valid for any ratio of the local surface curvature to the wave number. This is a generalization of the familiar Fresnel formula and Snell's law, valid at planar dielectric boundaries, for the scattering and transmission of electromagnetic waves at surfaces of arbitrary curvature. Implementation details are illustrated with scattering by multiple perfect electric conductors as well as dielectric bodies with complex geometries and composition.

We study the spin-orbit interaction effects in a one-dimensional electron system that result from the image charges in a nearby metallic gate. The nontrivial property of the image-potential-induced spin-orbit interaction (iSOI) is that it directly depends on the electron density because of which a positive feedback arises between the electron density and the iSOI magnitude. As a result, the system becomes unstable against the density fluctuations under certain conditions. In addition, the iSOI contributes to the electron-electron interaction giving rise to strong changes in electron correlations and collective excitation spectra. We trace the evolution of the spectrum of the collective excitations and their spin-charge structures with the change in the iSOI parameter. One out of two collective modes softens as the iSOI amplitude grows to become unstable at its critical value. Interestingly, this mode evolves from a pure spin excitation to a pure charge one. At the critical point its velocity turns to zero together with the charge stiffness.

Although Lorentz invariance forbids the presence of a term that tilts the energy-momentum relation in the Weyl Hamiltonian, a tilted dispersion is not forbidden and, in fact, generic for condensed matter realizations of Weyl semimetals. We here investigate the combined effect of such a tilted Weyl dispersion and the presence of potential disorder. In particular, we address the influence of a tilt on the disorder-induced phase transition between a quasiballistic phase at weak disorder, in which the disorder is an irrelevant perturbation, and a diffusive phase at strong disorder. Our main result is that the presence of a tilt leads to a reduction of the critical disorder strength for this transition or, equivalently, that increasing the tilt at fixed disorder strength drives the system through the phase transition to the diffusive strong-disorder phase. Notably this obscures the tilt-induced Lifshitz transition to an overtilted type II Weyl phase at any finite disorder strength. Our results are supported by analytical calculations using the self-consistent Born approximation and numerical calculations of the density of states and of transport properties.

We present a general treatment of carrier scattering by coupled phonon-plasmon collective modes in polar semiconductors, taking anharmonic phonon decay into account and self-consistently calculating carrier momentum relaxation rates and carrier mobility in a parabolic band model. We iteratively solve the weak-field Boltzmann equations for carriers and collective modes and obtain their nonequilibrium distribution functions. Both the scattering rates and the anharmonic decay of the coupled modes are expressed through the total dielectric function of the semiconductor, consisting of a damped lattice dielectric function, and a temperature dependent random phase approximation dielectric function for the carrier plasma. We show that the decay of the coupled modes has a significant effect on the contribution to the mobility limited by carrier-coupled mode scattering. We also propose a scalar quantity, the phonon dissipation weight factor, with which this effect can be estimated from an analytic expression. We apply this treatment to dynamically screened electron-longitudinal optical phonon scattering in bulk polar semiconductors, and to dynamically screened remote phonon scattering in polar heterostructures where monolayers of ${\mathrm{MoS}}_2$ are sandwiched between various polar dielectrics. We find that a dynamic treatment of the remote phonon scattering yields mobilities up to 75% higher than a static screening approximation does for structures which consist of a monolayer of ${\mathrm{MoS}}_2$ between hafnia and silica. Moreover, we show that accounting for the nonzero thickness of the ${\mathrm{MoS}}_2$ interface layer has an important effect on the calculated mobility in the same structure.

Room-temperature simulations of graphene have been performed as a function of the mechanical tension of the layer. Finite-size effects are accurately reproduced by an acoustic dispersion law for the out-of-plane vibrations that, in the long-wave limit, behaves as $\rho {\omega }^2=\sigma k^2+\kappa k^4$. The fluctuation tension $\sigma$ is finite ($\sim 0.1$ N/m) even when the external mechanical tension vanishes. Transverse vibrations imply a duplicity in the definition of the elastic constants of the layer, as observables related to the real area of the surface may differ from those related to the in-plane projected area. This duplicity explains the variability of experimental data on the Young modulus of graphene based on electron spectroscopy, interferometric profilometry, and indentation experiments.

In van der Waals multilayers of triangular lattice, trigonal warping occurs universally due to the interlayer hopping. We theoretically investigate the effect of trigonal warping upon distinctive topological phases, such as the quantum anomalous Hall effect (QAHE) and the quantum valley Hall effect (QVHE). Taking Bernal-stacked bilayer graphene as an example, we find that the trigonal warping plays a crucial role in the formation of QAHE in a large exchange field and/or interlayer potential difference by inducing extra band inversion points at a momentum further away from the high-symmetry point. The presence of trigonal warping shrinks the phase space of QAHE and QVHE, leading to the emergence of a valley-polarized QAHE with high Chern numbers ranging from $\mathcal{C}=-7$ to 7 . These results suggest that the universal trigonal warping may play an important role when the Bloch states at momenta deviated from high-symmetry points are involved.

This work investigates the high-pressure structure of $\mathrm{C}{\mathrm{s}}_2\mathrm{CoC}{\mathrm{l}}_4$ and how it affects the electronic and vibrational properties using optical absorption, Raman spectroscopy, x-ray diffraction, and x-ray absorption in the 0–15 GPa range. In particular, we focus on the electronic and local structures of $\mathrm{C}{\mathrm{o}}^{2+}$, since compression of $\mathrm{C}{\mathrm{s}}_2\mathrm{CoC}{\mathrm{l}}_4$ yields structural transformations associated with change of coordination around $\mathrm{C}{\mathrm{o}}^{2+}$, which are eventually responsible for the intense piezochromism at 7 GPa. This study provides a complete characterization of the electronic and vibrational structures of $\mathrm{C}{\mathrm{s}}_2\mathrm{CoC}{\mathrm{l}}_4$ in the Pnma phase as a function of the cell volume and the local $\mathrm{CoC}{\mathrm{l}}_4$ bond length, $R_{\text{Co-Cl}}$, as well as its corresponding equation of state. In addition, our interest is to elucidate whether the phase transition undergone by $\mathrm{C}{\mathrm{s}}_2\mathrm{CoC}{\mathrm{l}}_4$ at 7 GPa leads to a perovskite-layer-type structure where $\mathrm{C}{\mathrm{o}}^{2+}$ is sixfold coordinated, decomposes into $\mathrm{CsCl}+\mathrm{CsCoC}{\mathrm{l}}_3$, or it involves an unknown phase with different coordination sites for $\mathrm{C}{\mathrm{o}}^{2+}$. We show that $\mathrm{C}{\mathrm{o}}^{2+}$ is sixfold coordinated in the high-pressure phase. The analysis of optical spectra and x-ray diffraction data suggests the formation of an interconnected structure of exchange-coupled $\mathrm{C}{\mathrm{o}}^{2+}$ through edge-sharing octahedra at high pressure.

We use series expansion methods to investigate the phase diagram of a frustrated spin-$\frac{1}{2}$ Heisenberg antiferromagnet on the simple cubic lattice, with interactions extending to third neighbors. Our results do not support a recent prediction of a rather large paramagnetic phase at zero temperature, but do show behavior which may be indicative of a small disordered region near the point of maximum frustration.

In the spinel compound ${\mathrm{GeCo}}_2{\mathrm{O}}_4$, the ${\mathrm{Co}}^{2+}$ pyrochlore sublattice presents remarkable magnetic-field-induced behaviors that we unveil through neutron and x-ray single-crystal diffraction. The Néel-ordered magnetic phase is entered through a structural lowering of the cubic symmetry. In this phase, when a magnetic field is applied along a 2-fold cubic direction, a spin-flop transition of one-fourth of the magnetic moments releases the magnetic frustration and triggers magnetostructural effects. At high field, these ultimately lead to an unusual spin reorientation associated with structural changes.

Superconducting vortices and phase slips are primary mechanisms of dissipation in superconducting, superfluid, and cold-atom systems. While the dynamics of vortices is fairly well described, phase slips occurring in quasi-one-dimensional superconducting wires still elude understanding. The main reason is that phase slips are strongly nonlinear time-dependent phenomena that cannot be cast in terms of small perturbations of the superconducting state. Here we study phase slips occurring in superconducting weak links. Thanks to partial suppression of superconductivity in weak links, we employ a weakly nonlinear approximation for dynamic phase slips. This approximation is not valid for homogeneous superconducting wires and slabs. Using the numerical solution of the time-dependent Ginzburg-Landau equation and bifurcation analysis of stationary solutions, we show that the onset of phase slips occurs via an infinite period bifurcation, which is manifested in a specific voltage-current dependence. Our analytical results are in good agreement with simulations.

We show that topological phases should be realizable in readily available and well-studied heterostructures. In particular we identify a new class of topological materials which are well known in spintronics: helical ferromagnet-superconducting junctions. We note that almost all previous work on topological heterostructures has focused on creating Majorana modes at the proximity interface in effectively two-dimensional or one-dimensional systems. The particular heterostructures we address exhibit finite-range proximity effects leading to nodal superconductors with Majorana modes localized well away from this interface. To show this, we implement a Bogoliubov–de Gennes (BdG) proximity numerical scheme, which importantly involves two finite dimensions in a three-dimensional junction. Incorporating this level of numerical complexity serves to distinguish ours from alternative numerical BdG approaches which are limited by generally assuming translational invariance or periodic boundary conditions along multiple directions. With this access to the edges, we are then able to illustrate in a concrete fashion the wave functions of Majorana zero modes and, moreover, address finite-size effects. In the process we establish consistency with a simple analytical model.

Thermal fluctuations of the Josephson current induced by the magnetic flux through a ring of $N$ superconducting grains are studied. When a half-fluxon is threading the ring, $I$ exhibits incoherent transitions between the two degenerate states due to thermal phase slips. We propose a numerical method to deal with both equilibrium and dynamic properties of Josephson systems. Computed transition rate has the form $\mathrm{\Gamma }=A\left(N\right)exp[-B(N)/T]$, where $B\left(N\right)$ agrees with the analytical result derived for the energy barrier associated with phase slips. In the nondegenerate case (e.g., at a quarter-fluxon) the equilibrium value of $I$ decreases with $T$ due to harmonic excitations and then gets destroyed by phase slips.

We study one-dimensional spinless fermions with random interactions, but without any on-site disorder. We find that random interactions generically stabilize a many-body localized phase, in spite of the completely extended single-particle degrees of freedom. In the large randomness limit, we construct “bubble-neck” eigenstates having a universal area-law entanglement entropy on average, with the number of volume-law states being exponentially suppressed. We argue that this statistical localization is beyond the phenomenological local-integrals-of-motion description of many-body localization. With exact diagonalization, we confirm the robustness of the many-body localized phase at finite randomness by investigating eigenstate properties such as level statistics, entanglement/participation entropies, and nonergodic quantum dynamics. At weak random interactions, the system develops a thermalization transition when the single-particle hopping becomes dominant.