Many-body localized (MBL) systems are characterized by the absence of transport and thermalization and, therefore, cannot be described by conventional statistical mechanics. In this paper, using analytic arguments and numerical simulations, we study the behavior of local observables in an isolated MBL system following a quantum quench. For the case of a global quench, we find that the local observables reach stationary, highly nonthermal values at long times as a result of slow dephasing characteristic of the MBL phase. These stationary values retain the local memory of the initial state due to the existence of local integrals of motion in the MBL phase. The temporal fluctuations around stationary values exhibit universal power-law decay in time, with an exponent set by the localization length and the diagonal entropy of the initial state. Such a power-law decay holds for any local observable and is related to the logarithmic in time growth of entanglement in the MBL phase. This behavior distinguishes the MBL phase from both the Anderson insulator (where no stationary state is reached) and from the ergodic phase (where relaxation is expected to be exponential). For the case of a local quench, we also find a power-law approach of local observables to their stationary values when the system is prepared in a mixed state. Quench protocols considered in this paper can be naturally implemented in systems of ultracold atoms in disordered optical lattices, and the behavior of local observables provides a direct experimental signature of many-body localization.

The critical behavior near the continuous paramagnetic to ferromagnetic transition in a single crystal of ${\mathrm{La}}_{0.75}{\mathrm{Pr}}_{0.25}{\mathrm{Co}}_2{\mathrm{P}}_2$ has been determined based on high-resolution bulk magnetization data near $T_C$ ∼ 167 K, where long-range order is established in the Co sublattice. Scaling equation of state analysis and the Kouvel-Fisher method under a moderate applied magnetic field yielded critical exponents ($\beta =0.3685\pm 0.0017$, $\gamma =1.3361\pm 0.0083$), consistent with the $d$ = 3, $n$ = 3 Heisenberg model of short-range interactions. Calculation of the Rhodes-Wohlfarth ratio confirmed that a localized rather than itinerant description of the $3d$ Co moments is appropriate in the ferromagnetic region of the sample. The critical susceptibility exponent γ was found to decrease systematically from the Heisenberg model value toward the mean-field model value as the maximum applied magnetic field considered in the analysis was increased above 2 T. The phenomenon is discussed in terms of mixed exchange mechanisms due to the coexistence of $3d$ and $4f$ magnetic sublattices and ordered clusters in the paramagnetic region.

We study the magnetization dynamics of spin-torque oscillators in the presence of thermal noise and as a function of the spin-polarization angle in a macrospin model. The macrospin has biaxial magnetic anisotropy, typical of thin film magnetic elements, with an easy axis in the film plane and a hard axis out of the plane. Using a method that averages the energy over precessional orbits, we derive analytic expressions for the current that generates and sustains out-of-plane precessional states. We find that there is a critical angle of the spin polarization necessary for the occurrence of such states and predict a hysteretic response to applied current. This model can be tested in experiments on orthogonal spin-transfer devices, which consist of both an in-plane and out-of-plane magnetized spin polarizers, effectively leading to an angle between the easy and spin-polarization axes.

We present experimental and theoretical evidence that an interesting quantum many-body effect—quasiparticle breakdown—occurs in the quasi-one-dimensional spin-$\frac{1}{2}$ Ising-like ferromagnet ${\mathrm{CoNb}}_2{\mathrm{O}}_6$ in its paramagnetic phase at high transverse field as a result of explicit breaking of spin inversion symmetry. We propose a quantum spin Hamiltonian capturing the essential one-dimensional physics of ${\mathrm{CoNb}}_2{\mathrm{O}}_6$ and determine the exchange parameters of this model by fitting the calculated single-particle dispersion to the one observed experimentally in applied transverse magnetic fields [1]. We present high-resolution inelastic neutron scattering measurements of the single-particle dispersion which observe “anomalous broadening” effects over a narrow energy range at intermediate energies. We propose that this effect originates from the decay of the one particle mode into two-particle states. This decay arises from (i) a finite overlap between the one-particle dispersion and the two-particle continuum in a narrow energy-momentum range and (ii) a small misalignment of the applied field away from the direction perpendicular to the Ising axis in the experiments, which allows for nonzero matrix elements for decay by breaking the ${\mathbb{Z}}_2$ spin inversion symmetry of the Hamiltonian.

On the basis of group theory and first-principles calculations, we investigate high-rank multipole orderings in ${\mathrm{URu}}_2{\mathrm{Si}}_2$, which have been proposed as a genuine primary order parameter in the hidden-order phase below $17.5$ K. We apply Shubnikov group theory to the multipole ordered states characterized by the wave vector ${\mathit{Q}}_0=(0,0,1)$ and specify the global/site symmetry and the secondary order parameters, such as induced dipole moments and change in charge distribution. We find that such antiferroic magnetic multipole orderings are particularly advantageous to conceal the primary order parameter due to preserving high symmetry in charge distribution. Experimental observations of the induced low-rank multipoles, which are explicitly classified in this paper, will be key pieces to understand the puzzling hidden-order phase.

In their article, Zhang et al. [Phys. Rev. B 86, 024516 (2012)] present a remarkable result for $A_x{\left(S\right)}_y\mathrm{TiNCl}$ compounds ($\alpha$-phase TiNCl partially intercalated with alkali $A$ and optionally co-intercalated molecular species $S$), finding the superconducting transition temperature $T_c$ scales with $d^{-1}$, where the spacing $d$ between TiNCl-layered structures depends on intercalant thickness. Recognizing that this behavior indicates interlayer coupling, Zhang et al. cite, among other papers, the interlayer Coulombic pairing mechanism picture [Harshman et al., J. Phys.: Condens. Matter 23, 295701 (2011)]. This Comment shows that superconductivity occurs by interactions between the chlorine layers of the TiNCl structure and the layers containing $A_x$, wherein the transverse $A_x\text{−}\mathrm{Cl}$ separation distance $\zeta$ is smaller than $d$. In the absence of pair-breaking interactions, the optimal transition temperature is modeled by $T_{c0}\propto {\left(\sigma /A\right)}^{1/2}{\zeta }^{-1}$, where $\sigma /A$ is the fractional charge per area per formula unit. Particularly noteworthy are the rather marginally metallic trends in resistivities of $A_x{\left(S\right)}_y\mathrm{TiNCl}$, indicating high scattering rates, which are expected to partially originate from remote Coulomb scattering (RCS) from the $A_x$ ions. By modeling a small fraction of the RCS as inducing pair breaking, taken to cut off exponentially with $\zeta$, observations of $T_c<T_{c0}$ are quantitatively described for compounds with $\zeta <4\AA$ and $T_c\approx T_{c0}$ for $\mathrm{N}{\mathrm{a}}_{0.16}{\left(S\right)}_y\mathrm{TiNCl}$ with propylene carbonate and butylene carbonate co-intercalants for which $\zeta >7\AA$. Since a spatially separated alkali-ion layer is not formed in $\mathrm{L}{\mathrm{i}}_{0.13}\mathrm{TiNCl}$, the observed $T_c$ of 5.9 K is attributed to an intergrowth phase related to TiN $\left(T_c=5.6\mathrm{K}\right)$.

We have studied the electron-doped $\alpha$-form TiNCl (FeOCl orthorhombic type) in detail and have found the transition temperature $T_c$ of 18.0 K decreases monotonically with increasing the interlayer spacing $d$ upon co-intercalation of various kinds of organic solvent molecules with alkali atoms. We conclude that such kinds of experimental results imply the importance of interlayer Coulomb coupling [Phys. Rev. B 86, 024516 (2012)], which is a strong contrast to the behavior previously found in the electron doped $\beta$-form ZrNCl and HfNCl. In their Comment, Harshman and Fiory [Phys. Rev. B 90, 186501 (2014)] discuss a detailed model with remote Coulomb scattering to scale the optimized $T_c$, which is consistent with our conclusion.

The Berry phase on the Fermi surface and its influence on the conserved spin current in a two-dimensional system with generic $k$-linear spin-orbit interaction are investigated. We calculate the response of the effective conserved spin current to the applied electric field, which is composed of conventional and spin-torque currents by using the Kubo formula. We find that the conventional spin current is not determined by the Berry-phase effect. Remarkably, the spin-torque Hall current is found to be proportional to the Berry phase, and the longitudinal spin-torque current vanishes because of the Berry-phase effect. When the $k$-linear spin-orbit interaction dominates the system, the Berry phase on the Fermi surface maintains two invariant properties. One is that the magnitude of the spin-torque current protected by the Berry phase is unchanged by a small fluctuation in energy dispersion. The other one is that the change in the direction of the applied electric field does not change the magnitude of the spin-torque current even if the energy dispersion is not spherically symmetric, i.e., the Berry-phase effect has no dependence on the two-dimensional material orientation. The spin-torque current is a universal value for all $k$-linear systems, such as Rashba, Dresselhaus, and Rashba-Dresselhaus systems. The topological number attributed to the Berry phase on the Fermi surface represents the phase of the orbital chirality of spin in the $k$-linear system. The change in the topological number results in a phase transition in which the orbital chirality of spins $s_z$ and $-s_z$ is exchanged. We found that the spin-torque current can be experimentally measured.

Edge excitations of the $\nu =0$ quantum Hall state in monolayer graphene are studied within the mean-field theory with different symmetry-breaking terms. The analytical expressions for the continuum (Dirac) model wave functions are obtained for the charge density wave, Kekulé distortion, ferromagnetic, and (canted) antiferromagnetic phases. The dispersion equations for each phase and boundary type (zigzag and armchair) are derived, numerically solved, and compared to the results of the corresponding effective tight-binding model. The effect of the next-to-nearest neighbor hopping parameter on the edge state spectrum is studied and revealed to be essential. The criteria for the existence of gapless edge states are established for each phase and edge type.

We have investigated electron transport in a quasi-one dimensional (quasi-1D) electron gas as a function of the confinement potential. At a particular potential configuration, and electron concentration, the ground state of a 1D quantum wire splits into two rows to form an incipient Wigner lattice. It was found that application of a transverse magnetic field can transform a double-row electron configuration into a single row due to magnetic enhancement of the confinement potential. The movements of the energy levels have been monitored under varying conditions of confinement potential and in-plane magnetic field. It is also shown that when the confinement is weak, electron occupation drives a reordering of the levels such that the normal ground state passes through the higher levels. The results show that the levels can be manipulated by utilizing their different dependence on spatial confinement and electron concentration, thus enhancing the understanding of many-body interactions in mesoscopic 1D quantum wires.

The photoexcited dynamics of the order parameter in a Peierls chain is investigated by using a microscopic quantum theory in the limit where the hot electrons may establish themselves into a quasi-equilibrium state described by an effective temperature. The optical phonon mode responsible for the Peierls instability is coupled to the electron subsystem, and its dynamic equation is derived in terms of the density matrix technique. Recovery dynamics of the order parameter is obtained, which reveals a number of interesting features including the change of oscillation frequency and amplitude at the phase-transition temperature and the photoinduced switching of the order parameter.

Temperature dependent optical reflectance measurements on well characterized samples of nonintentionally doped, Cr-doped, and V-doped ${\mathrm{Sb}}_2{\mathrm{Te}}_3$ show that both the parent compound and the Cr-doped version are narrow-gap semiconductors $(E_g\approx 0.25$ eV) with a conventional Drude free carrier absorption. The carrier density increases slightly with decreasing temperature while the scattering rate increases quadratically with temperature, which is a sign of the importance of optical phonon scattering. Vanadium doping introduces a change in the temperature dependence of the scattering rate as well as higher electrical resistivity than Cr-doped ${\mathrm{Sb}}_2{\mathrm{Te}}_3$. An analysis of the literature values of the saturation magnetization of ${\mathrm{Sb}}_{2-x}{\mathrm{V}}_x{\mathrm{Te}}_3$ for $H\parallel c$ suggests V is in a mixed valence state ${\mathrm{V}}^{3+}/{\mathrm{V}}^{4+}$.

We study the dynamics of a quantum spin Hall edge coupled to a magnet with its own dynamics. Using spin-transfer-torque principles, we analyze the interplay between spin currents in the edge state and dynamics of the axis of the magnet, and draw parallels with circuit analogies. As a highlighting feature, we show that while coupling to a magnet typically renders the edge state insulating by opening a gap, in the presence of a small potential bias, spin-transfer torque can restore perfect conductance by transferring angular momentum to the magnet. In the presence of interactions within the edge state, we employ a Luttinger liquid treatment to show that the edge, when subject to a small voltage bias, tends to form a unique dynamic rotating spin wave state that naturally couples into the dynamics of the magnet. We briefly discuss realistic physical parameters and constraints for observing this interplay between quantum spin Hall and spin-transfer torque physics.

Resolving atomic-scale defect topologies and energetics with accurate atomistic interaction models provides access to the nonlinear phenomena inherent at atomic length and time scales. Coarse graining the dynamics of such simulations to look at the migration of, e.g., solute atoms, while retaining the rich atomic-scale detail required to properly describe defects, is a particular challenge. In this paper, we present an adaptation of the recently developed “diffusive molecular dynamics” model to describe the energetics and kinetics of binary alloys on diffusive time scales. The potential of the technique is illustrated by applying it to the classic problems of solute segregation to a planar boundary (stacking fault) and edge dislocation in the Al-Mg system. Our approach provides fully dynamical solutions in situations with an evolving energy landscape in a computationally efficient way, where atomistic kinetic Monte Carlo simulations are difficult or impractical to perform.

Halogen vacancies (${\mathit{V}}_{\mathrm{H}}$) are usually deep color centers (F centers) in halides and can act as major electron traps or recombination centers. The deep ${\mathit{V}}_{\mathrm{H}}$ contributes to the typically poor carrier transport properties in halides. However, several halides have recently emerged as excellent optoelectronic materials, e.g., $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3\mathrm{Pb}{\mathrm{I}}_3$ and TlBr. Both $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3\mathrm{Pb}{\mathrm{I}}_3$ and TlBr have been found to have shallow ${\mathit{V}}_{\mathrm{H}}$, in contrast to commonly seen deep ${\mathit{V}}_{\mathrm{H}}$ in halides. In this paper, several halide optoelectronic materials, i.e., $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3\mathrm{Pb}{\mathrm{I}}_3$, $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3\mathrm{Sn}{\mathrm{I}}_3$ (photovoltaic materials), TlBr, and $\mathrm{CsPbB}{\mathrm{r}}_3$ (gamma-ray detection materials) are studied to understand the material chemistry and structure that determine whether ${\mathit{V}}_{\mathrm{H}}$ is a shallow or deep defect in a halide material. It is found that crystal structure and chemistry of $n{s}^2$ ions both play important roles in creating shallow ${\mathit{V}}_{\mathrm{H}}$ in halides such as $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3\mathrm{Pb}{\mathrm{I}}_3$, $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3\mathrm{Sn}{\mathrm{I}}_3$, and TlBr. The key to identifying halides with shallow ${\mathit{V}}_{\mathrm{H}}$ is to find the right crystal structures and compounds that suppress cation orbital hybridization at ${\mathit{V}}_{\mathrm{H}}$, such as those with large cation-cation distances and low anion coordination numbers and those with crystal symmetry that prevents strong hybridization of cation dangling bond orbitals at ${\mathit{V}}_{\mathrm{H}}$. The results of this paper provide insight and guidance to identifying halides with shallow ${\mathit{V}}_{\mathrm{H}}$ as good electronic and optoelectronic materials.

The dynamical and thermodynamic phase stabilities of the stoichiometric compound CrN including different structural and magnetic configurations are comprehensively investigated using a first-principles density functional theory (DFT) plus $U$ ($\mathrm{DFT}+U$) approach in conjunction with experimental measurements of the thermal expansion. Comparing DFT and $\mathrm{DFT}+U$ results with experimental data reveals that the treatment of electron correlations using methods beyond standard DFT is crucial. The nonmagnetic face-centered cubic B1-CrN phase is both elastically and dynamically unstable, even under high pressure, while CrN phases with nonzero local magnetic moments are predicted to be dynamically stable within the framework of the $\mathrm{DFT}+U$ scheme. Furthermore, the impact of different treatments for the exchange-correlation (xc)-functional is investigated by carrying out all computations employing the local density approximation and generalized gradient approximation. To address finite-temperature properties, both magnetic and vibrational contributions to the free energy have been computed employing our recently developed spin-space averaging method. The calculated phase transition temperature between low-temperature antiferromagnetic and high-temperature paramagnetic (PM) CrN variants is in excellent agreement with experimental values and reveals the strong impact of the choice of the xc-functional. The temperature-dependent linear thermal expansion coefficient of CrN is experimentally determined by the wafer curvature method from a reactive magnetron sputter deposited single-phase B1-CrN thin film with dense film morphology. A good agreement is found between experimental and ab initio calculated linear thermal expansion coefficients of PM B1-CrN. Other thermodynamic properties, such as the specific heat capacity, have been computed as well and compared to previous experimental data.

Using the examples of laser-induced spin-reorientation phase transitions in ${\mathrm{TmFeO}}_3$ and ${\mathrm{ErFeO}}_3$ orthoferrites, we demonstrate that terahertz emission spectroscopy can obtain novel information about ultrafast laser-induced spin dynamics, which is not accessible by more common all-optical methods. The power of the method is evidenced by the fact that, in addition to the expected quasi-ferromagnetic and quasi-antiferromagnetic modes of the iron sublattices, terahertz emission spectroscopy enables detection of a resonance optically excited at an unexpected frequency of ∼0.3–0.35 THz. By recording how the amplitude and phase of the excited oscillations depend on temperature and applied magnetic field, we show that the unexpected mode has all the features of a spin resonance of the ${\mathrm{Fe}}^{3+}$ ions. We suggest that it can be assigned to transitions between the multiplet sublevels of the ${}^6{A}_1$ ground state of the ${\mathrm{Fe}}^{+3}$ ions occupying rare-earth positions.

Recent pump-probe experiments provide time evolution of the bulk and surface electronic states in Gd excited by the laser pulse. These experiments are in close connection with earlier spectroscopic experiments probing temperature dependence of the exchange splitting of the electronic states. We report first-principles study of the electronic states in excited Gd modeled by the noncollinearity of the $4f$ spin moments. In agreement with experiments we obtain a strong difference in the properties of the bulk and surface electronic states. To reveal the origin of this behavior we apply the concept of spin mixing to characterize the electronic states of the excited system. The surface states remain weakly spin mixed with respect to the local atomic spin axis of the surface layer that explains the persistence of the exchange splitting in highly excited Gd. On the other hand, a smaller part of the surface state localized in the second layer becomes strongly spin mixed leading to decreased value of the exchange splitting. In contrast to the surface states the bulk states are strongly spin mixed and average the influence of the atomic spin-up and spin-down potentials. This leads to the properties of the bulk states that are usually associated with the Stoner model. The good agreement between calculational results and the results of the pump-probe experiment support the assumption of ultrafast disordering of the $4f$ moments after laser irradiation.

We investigate the equilibrium and nonequilibrium transport through a quantum dot in the Kondo regime, embedded between a normal metal and a topological superconductor supporting Majorana bound states at its end points. We find that the Kondo physics is significantly modified by the presence of the Majorana modes. When the Majorana modes are coupled, aside from the Kondo scale $T_K$, a new energy scale $T^{*}\ll T_K$ emerges, that controls the low-energy physics of the system. At low temperatures, the ac conductance is suppressed for frequencies below $T^{*}$, while the noise spectrum acquires a $\sim {\omega }^3$ dependence. At high temperatures, $T\gg T_K$, the regular logarithmic dependence in the differential conductance is also affected. Under nonequilibrium conditions, and in particular in the $\{T,B\}\to 0$ limit, the differential conductance becomes negative. These findings indicate that the changes in transport may serve as clues for detecting the Majorana bound states in such systems. In terms of methods used, we characterize the transport by using a combination of perturbative and renormalization-group approaches.