We study spin-orbit torques (SOT) in nondegenerate multiband electron systems in the weak-disorder limit. In order to have better physical transparency, a semiclassical Boltzmann approach equivalent to the Kubo diagrammatic approach in the noncrossing approximation is formulated. This semiclassical framework accounts for the interband-coherence effects induced by both the electric field and static impurity scattering. Using the two-dimensional Rashba ferromagnet as a model system, we show that the antidamping-like SOT arising from disorder-induced interband-coherence effects is very sensitive to the structure of disorder potential in the internal space and may have the same sign as the intrinsic SOT in the presence of spin-dependent disorder. While the cancellation of this SOT and the intrinsic one occurs only in the case of spin-independent short-range disorder.

We study the quantum transport and the nonequilibrium vibrational states of a quantum dot embedded between a normal-conducting and a superconducting lead with the charge on the quantum dot linearly coupled to a harmonic oscillator of frequency $\omega$. To the leading order in the charge-vibration interaction, we calculate the current and the nonequilibrium phonon occupation by the Keldsyh Green's function technique. We analyze the inelastic, vibration-assisted tunneling processes in the regime $\omega <\mathrm{\Delta }$, with the superconducting energy gap $\mathrm{\Delta }$, and for sharp resonant transmission through the dot. When the energy ${\varepsilon }_0$ of the dot's level is close to the Fermi energy $\mu$, i.e., $|{\varepsilon }_0-\mu |\ll \mathrm{\Delta }$, inelastic vibration-assisted Andreev reflections dominate up to voltage $eV\gtrsim \mathrm{\Delta }$. The inelastic quasiparticle tunneling becomes the leading process when the dot's level is close to the superconducting gap $|{\varepsilon }_0-\mu |\sim \mathrm{\Delta }\pm \omega$. In both cases, the inelastic tunneling processes appear as sharp and prominent peaks—not broadened by temperature—in the current-voltage characteristic and pave the way for inelastic spectroscopy of vibrational modes even at temperatures $T\gg \omega$. We also found that inelastic vibration-assisted Andreev reflections as well as quasiparticle tunneling induce a strong nonequilibrium state of the oscillator. In different ranges on the dot's level, we found that the current produces: (i) ground-state cooling of the oscillator with phonon occupation $n\ll 1$, (ii) accumulation of energy in the oscillator with $n\gg 1$, and (iii) a mechanical instability characterized by a negative damping coefficient. We show that ground-state cooling is achieved simultaneously for several modes of different frequencies. Finally, we discuss how the nonequilibrium vibrational state can be readily detected by the asymmetric behavior of the inelastic current peaks with respect to the gate voltage.

Tin chains grown on the Si(100)$2\times 1$ surface were studied by scanning tunneling microscopy. Real time measurements were used for recording chain length fluctuations in a temperature range from 310 to 350 K. The recorded data were analyzed by means of a statistical model containing both interfering processes observed at a chain termination—random attachment and detachment of metal atoms. Rates of the both processes were calculated from lifetimes of two different chain terminations (monomer or dimer) by means of derived formulas. The activation energies for the detachment and frequency prefactors were calculated from dependence of the corresponding time constants on temperature in an Arrhenius plot. A similar approach was used for characterization of binding Sn atoms on $C$-type defects which represent preferential adsorption sites.

Machine-learning potentials (MLPs) for atomistic simulations are a promising alternative to conventional classical potentials. Current approaches rely on descriptors of the local atomic environment with dimensions that increase quadratically with the number of chemical species. In this paper, we demonstrate that such a scaling can be avoided in practice. We show that a mathematically simple and computationally efficient descriptor with constant complexity is sufficient to represent transition-metal oxide compositions and biomolecules containing 11 chemical species with a precision of around 3 meV/atom. This insight removes a perceived bound on the utility of MLPs and paves the way to investigate the physics of previously inaccessible materials with more than ten chemical species.

Although, as part of a general phenomenon, the piezoelectric response of $\mathrm{Ba}\left(\mathrm{T}{\mathrm{i}}_{1-y}{M}_y\right){\mathrm{O}}_3$ ($M=\mathrm{Zr}$, Sn, Hf) increases in the vicinity of the orthorhombic ($Amm2$)-tetragonal ($P4mm$) and orthorhombic ($Amm2$)-rhombohedral ($R3m$) polymorphic phase boundaries, experiments in the last few years have shown that the same phase boundaries show significantly enhanced weak-field piezoproperties in the Ca-modified variants of these ferroelectric alloys, i.e., $\left(\mathrm{Ba},\mathrm{Ca}\right)\left(\mathrm{Ti},M\right){\mathrm{O}}_3$. So far there is a lack of clarity with regard to the unique feature(s) which Ca modification brings about that enables this significant enhancement. Here, we examine this issue from a structural standpoint with $M=\mathrm{Sn}$ as a case study. We carried out a comprehensive comparative structural, ferroelectric, and piezoelectric analysis of the $Amm2$ phase in the immediate vicinity of the $P4mm\text{−}Amm2$ phase boundaries of (i) Ca-modified $\mathrm{Ba}\left(\mathrm{Ti},\mathrm{Sn}\right){\mathrm{O}}_3$, as per the nominal formula $\left(1-x\right)\mathrm{BaT}{\mathrm{i}}_{0.88}\mathrm{S}{\mathrm{n}}_{0.12}{\mathrm{O}}_3\text{−}\left(x\right)\mathrm{B}{\mathrm{a}}_{0.7}\mathrm{C}{\mathrm{a}}_{0.3}\mathrm{Ti}{\mathrm{O}}_3$ and (ii) without Ca modification, i.e., $\mathrm{Ba}\left(\mathrm{T}{\mathrm{i}}_{1-y}\mathrm{S}{\mathrm{n}}_y\right){\mathrm{O}}_3$. We found that the spontaneous lattice strain of the $Amm2$ phase is noticeably smaller in the Ca-modified counterpart. Interestingly, this happens along with an improved spontaneous polarization by enhancing the covalent character of the Ti-O bond. Our study suggests that the unique role of Ca modification lies in its ability to induce these seemingly contrasting features (reduction in spontaneous lattice strain but increase in polarization).

We investigate the phenomenon of spatial many-body localization (MBL) through pairwise correlation measures based on one- and two-point correlation functions. The system considered is the Heisenberg spin-1/2 chain with exchange interaction $J$ and random on-site disorder of strength $h$. As a representative pairwise correlation measure obtained from one-point functions, we use global entanglement. Through its finite-size-scaling analysis, we locate the MBL critical point at $h_c/J=3.8$. As for measures involving two-point functions, we analyze pairwise geometric classical, quantum, and total correlations. Similarly to what happens for continuous quantum phase transitions, it is the derivatives of these two-point correlation measures that identify the MBL critical point, which is found to be in the range $h_c/J\in [3,4]$. Our approach relies on very simple measures that do not require access to multipartite entanglement or large portions of the system.

In a recent letter [J. Cardy, Phys. Rev. Lett. 112, 220401 (2014)], the author made a very interesting observation that complete revivals of quantum states after quantum quench can happen in a period that is a fraction of the system size. This is possible for critical systems that can be described by minimal conformal field theories with central charge $c<1$. In this paper, we show that these complete revivals are impossible in microscopic realizations of those minimal models. We will prove the absence of the mentioned complete revivals for the critical transverse field Ising chain analytically, and present numerical results for the critical line of the XY chain. In particular, for the considered initial states, we will show that criticality has no significant effect in partial revivals. We also comment on the applicability of quasiparticle picture to determine the period of the partial revivals qualitatively. In particular, we detect a regime in the phase diagram of the XY chain in which one can not determine the period of the partial revivals using the quasiparticle picture.

We identified quasiparticle states at well-defined energies inside the superconducting gap of the electron system at the ${\mathrm{LaAlO}}_3\text{−}{\mathrm{SrTiO}}_3$ interface using tunneling spectroscopy. The states are found only in a number of samples and depend upon the thermal-cycling history of the samples. The states consist of a peak at zero energy and other peaks at finite energies, symmetrically placed around zero energy. These peaks disappear, together with the superconducting gap, with increasing temperature and magnetic field. We discuss the likelihood of various physical mechanisms that are known to cause in-gap states in superconductors and conclude that none of these mechanisms can easily explain the results. The conceivable scenarios are the formation of Majorana bound states, Andreev bound states, or the presence of an odd-frequency spin triplet component in the superconducting order parameter.

Interactions are responsible for intriguing physics, e.g., the emergence of exotic ground states and excitations, in a wide range of systems. Here, we theoretically demonstrate that dipole-dipole interactions lead to bosonic eigenexcitations with average spin ranging from zero to above $\hslash$ in magnets with uniformly magnetized ground states. These exotic excitations can be interpreted as quantum coherent conglomerates of spin $\hslash$ magnons, the eigenexcitations when the dipolar interactions are disregarded. We further find that the eigenmodes in an easy-axis antiferromagnet are spin-zero quasiparticles instead of the widely believed spin $\pm \hslash$ magnons. The latter reemerge when the symmetry is broken by a sufficiently large applied magnetic field. The average spin greater than $\hslash$ is accompanied by vacuum fluctuations and may be considered to be a weak form of frustration.

Motivated by the proposal of a topological quantum paramagnet in the diamond lattice antiferromagnet ${\mathrm{NiRh}}_2{\mathrm{O}}_4$, we propose a minimal model to describe the magnetic interaction and properties of the diamond material with spin-one local moments. Our model includes the first- and second-neighbor Heisenberg interactions as well as a local single-ion spin anisotropy that is allowed by the spin-one nature of the local moment and the tetragonal symmetry of the system. We point out that there exists a quantum phase transition from a trivial quantum paramagnet when single-ion spin anisotropy is dominant to the magnetic ordered states when the exchange is dominant. Due to the frustrated spin interaction, the magnetic excitation in the quantum paramagnetic state supports extensively degenerate band minima in the spectra. As the system approaches the transition, extensively degenerate bosonic modes become critical at the criticality, giving rise to unusual magnetic properties. Our phase diagram and experimental predictions for different phases provide a guideline for the identification of the ground state for ${\mathrm{NiRh}}_2{\mathrm{O}}_4$. Although our results are fundamentally different from the proposal for topological quantum paramagnets, they represent interesting possibilities for spin-one diamond lattice antiferromagnets.

We study the evolution of helical magnetism in MnGe chiral magnet upon partial substitution of Mn for $3d$-Co and $4d$-Rh ions. At high doping levels, we observe spin helices with very long periods—more than ten times larger than in the pure compound—and sizable ordered moments. This behavior calls for a change in the energy balance of interactions leading to the stabilization of the observed magnetic structures. Strikingly, neutron scattering unambiguously shows a double periodicity in the observed spectra at $x=0.5$ and >0.2 for Co- and Rh-doping, respectively. In analogy with observations made in smectic liquid crystals, we suggest that it may reveal the presence of magnetic “twist grain boundary” phases, involving a dense short-range correlated network of magnetic screw dislocations. The dislocation cores are here tentatively described as smooth textures, made of nonradial double-core skyrmions.

Recent advances in time-domain terahertz (THz) spectroscopy have unveiled that resonantly enhanced strong THz third-harmonic generation (THG) mediated by the collective Higgs amplitude mode occurs in $s$-wave superconductors, where charge-density fluctuations (CDFs) have been shown to also contribute to the nonlinear third-order susceptibility. It has been theoretically proposed that the nonlinear responses of Higgs and CDF exhibit essentially different polarization dependences. Here we experimentally discriminate the two contributions by polarization-resolved intense THz transmission spectroscopy for a single-crystal NbN film. The result shows that the resonant THG in the transmitted light always appears in the polarization parallel to that of the incident light with no appreciable polarization-angle dependence relative to the crystal axis. When we compare this with the theoretical calculation here with the BCS approximation and the dynamical mean-field theory for a model of NbN constructed from first principles, the experimental result strongly indicates that the Higgs mode rather than the CDF dominates the THG resonance in NbN. A possible mechanism for this is the retardation effect in the phonon-mediated pairing interaction beyond BCS.

The magnetic domain and bubble structures in the Z-type hexaferrite $\mathrm{S}{\mathrm{r}}_3\mathrm{C}{\mathrm{o}}_2\mathrm{F}{\mathrm{e}}_{24}{\mathrm{O}}_{41}$ were investigated using Lorentz microscopy. This hexaferrite exhibits a room-temperature magnetoelectric effect that is attributed to its transverse conical spin structure (TC phase). Upon heating, the TC phase transforms into a ferrimagnetic phase with magnetic moments in the hexagonal $ab$ plane between 410 and 480 K (FM2 phase) and into another ferrimagnetic phase with moments parallel to the $c$ axis between 490 and 680 K (FM1 phase). Accordingly, in this study, the magnetic domain structures in $\mathrm{S}{\mathrm{r}}_3\mathrm{C}{\mathrm{o}}_2\mathrm{F}{\mathrm{e}}_{24}{\mathrm{O}}_{41}$ were observed to change dramatically with temperature. In the TC phase, irregular fine magnetic domains were observed after cooling the specimen from the FM2 to TC phase. In the FM1 phase, striped magnetic domain walls with pairs of bright and dark contrast were formed parallel to the $c$ axis. Upon applying an external magnetic field, the striped magnetic domain walls transformed into magnetic bubbles. The topology of the magnetic bubbles was dependent on the angle between the external magnetic field $\left(H\right)$ direction and the easy $c$ axis. Namely, magnetic bubbles with the topological number $N=1$ (type I) were created for $H\parallel c$, whereas magnetic bubbles with $N=0$ (type II) were created when the magnetic field was tilted from the $c$ axis by $5^{\circ }$. We attribute the high magnetocrystalline anisotropy of $\mathrm{S}{\mathrm{r}}_3\mathrm{C}{\mathrm{o}}_2\mathrm{F}{\mathrm{e}}_{24}{\mathrm{O}}_{41}$ to the emergence of magnetic bubbles in the FM1 phase.

The electronic and thermal transport properties of the Earth's core are crucial for many geophysical models such as the geodynamo model of the Earth's magnetic field and of its reversals. Here we show, by considering bcc iron and an iron-rich iron-silicon alloy as a representative of the Earth's core composition and applying first-principles modeling, that the spin disorder at the Earth's core conditions not considered previously provides an essential contribution, of order 20 $\mu \mathrm{\Omega }$ cm, to the electrical resistivity. This value is comparable in magnitude with the electron-phonon and with the recently estimated electron-electron scattering contributions. The origin of the spin-disorder resistivity (SDR) consists of the existence of fluctuating local moments that are stabilized at high temperatures by the magnetic entropy even at pressures at which the ground state of iron is nonmagnetic. We find that electron-phonon and SDR contributions are not additive at high temperatures. We thus observe a large violation of the Matthiessen rule, not common in conventional metallic alloys at ambient conditions.

Recent angle-resolved spectroscopy in ${\mathrm{BiS}}_2$-based superconductors has indicated that the superconducting gap amplitude possesses remarkable anisotropy and/or a sign change on a small Fermi pocket around the $X$ point. It implies a possibility of an unconventional pairing state. Here we study the gap anisotropy in superconductivity mediated by inherent charge and quadrupole fluctuations in an extended Hubbard model, which includes intersite interaction between Bi and S atoms. The first-principles downfolded band structure is composed of Bi $6p_x/p_y$ and S $3p_x/p_y$ orbitals on a ${\mathrm{BiS}}_2$ single layer. Evaluating the linearized gap equation, we find that the ferroic charge and quadrupole fluctuation driven by the intersite interaction leads to a fully gapped $d_{x^2-y^2}$-wave pairing state, in which the gap amplitude has sizable anisotropy on the Fermi surface.

A semirelativistic density-functional theory that includes spin-orbit couplings and Zeeman fields on equal footing with the electromagnetic potentials, is an appealing framework to develop a unified first-principles computational approach for noncollinear magnetism, spintronics, orbitronics, and topological states. The basic variables of this theory include the paramagnetic current and the spin-current density, besides the particle and the spin density, and the corresponding exchange-correlation (xc) energy functional is invariant under local $\mathrm{U}\left(1\right)\times \mathrm{SU}\left(2\right)$ gauge transformations. The xc-energy functional must be approximated to enable practical applications, but, contrary to the case of the standard density functional theory, finding simple approximations suited to deal with realistic atomistic inhomogeneities has been a long-standing challenge. Here we propose a way out of this impasse by showing that approximate gauge-invariant functionals can be easily generated from existing approximate functionals of ordinary density-functional theory by applying a simple minimal substitution on the kinetic energy density, which controls the short-range behavior of the exchange hole. Our proposal opens the way to the construction of approximate, yet nonempirical functionals, which do not assume weak inhomogeneity and therefore may have a wide range of applicability in atomic, molecular, and condensed matter physics.

The coherent optical response from 140 nm and 65 nm thick ZnO epitaxial layers is studied using four-wave-mixing spectroscopy with picosecond temporal resolution. Resonant excitation of neutral donor-bound excitons results in two-pulse and three-pulse photon echoes. For the donor-bound A exciton (${\mathrm{D}}^0{\mathrm{X}}_{\text{A}}$) at temperature of 1.8 K we evaluate optical coherence times $T_2=33–50$ ps corresponding to homogeneous line widths of $13–19\mu \mathrm{eV}$, about two orders of magnitude smaller as compared with the inhomogeneous broadening of the optical transitions. The coherent dynamics is determined mainly by the population decay with time $T_1=30–40$ ps, while pure dephasing is negligible. Temperature increase leads to a significant shortening of $T_2$ due to interaction with acoustic phonons. In contrast, the loss of coherence of the donor-bound B exciton (${\mathrm{D}}^0{\mathrm{X}}_{\text{B}}$) is significantly faster ($T_2=3.6\mathrm{ps}$) and governed by pure dephasing processes.

Using analytical arguments and computer simulations, we show that the dependence of the hopping carrier mobility on the electric field $\mu \left(F\right)/\mu \left(0\right)$ in a system of random sites is determined by the localization length $a$, and not by the concentration of sites $N$. This result is in drastic contrast to what is usually assumed in the literature for a theoretical description of experimental data and for device modeling, where $N^{-1/3}$ is considered as the decisive length scale for $\mu \left(F\right)$. We show that although the limiting value $\mu (F\to 0)$ is determined by the ratio $N^{-1/3}/a$, the dependence $\mu \left(F\right)/\mu \left(0\right)$ is sensitive to the magnitude of $a$, and not to $N^{-1/3}$. Furthermore, our numerical and analytical results prove that the effective temperature responsible for the combined effect of the electric field $F$ and the real temperature $T$ on the hopping transport via spatially random sites can contain the electric field only in the combination $eFa$.

A hard proximity-induced superconducting gap has recently been observed in semiconductor nanowire systems at low magnetic fields. However, in the topological regime at high magnetic fields, a soft gap emerges and represents a fundamental obstacle to topologically protected quantum information processing with Majorana bound states. Here we show that in a setup of double Rashba nanowires that are coupled to an $s$-wave superconductor and subjected to an external magnetic field along the wires, the topological threshold can be significantly reduced by the destructive interference of direct and crossed-Andreev pairing in this setup, precisely down to the magnetic field regime in which current experimental technology allows for a hard superconducting gap. We also show that the resulting Majorana bound states exhibit sufficiently short localization lengths, which makes them ideal candidates for future braiding experiments.

All-optical femtosecond relaxation dynamics in a single crystal of monophosphate tungsten bronze $({\mathrm{PO}}_2{)}_4{\left({\mathrm{WO}}_3\right)}_{2m}$ with alternate stacking $m=6$ of ${\mathrm{WO}}_3$ layers was studied through the three consequent charge-density-wave (CDW) transitions. Several transient coherent collective modes associated with the different CDW transitions were observed and analyzed in the framework of the time-dependent Ginzburg–Landau theory. Remarkably, the interference of the modes leads to an apparent rectification effect in the transient reflectivity response. A saturation of the coherent-mode amplitudes with increasing pump fluence well below the CDWs destruction threshold fluence indicates a decoupling of the electronic and lattice parts of the order parameter on the femtosecond timescale.