We present a cluster expansion method for approximating quantum spin-bath dynamics in terms of a classical Gaussian stochastic process. The cluster expansion produces the two-point correlation function of the approximate classical bath, permitting rapid evaluation of noise-mitigating quantum control strategies without resorting to computationally intensive dynamical decoupling models. Our approximation is valid for the wide class of models possessing negligible back-action and nearly-Gaussian noise. We study several instances of the central spin decoherence problem in which the central spin and randomly-located bath spins are alike and dipolarly coupled. For various pulse sequences, we compare the coherence echo decay computed explicitly quantum mechanically versus those computed using our approximate classical model, and obtain agreement in most, but not all, cases. We demonstrate the utility of these classical noise models by efficiently searching for the 4-pulse sequences that maximally mitigate decoherence in each of these cases, a computationally expensive task in the explicit quantum model.

Recently, enhancement of the longitudinal magnetoelectrical conductivity (LMEC) has been observed in ${\mathrm{Bi}}_{1-x}{\mathrm{Sb}}_x$ around $x\sim 3\%$ under $\mathit{E}\parallel \mathit{B}$ ($\mathit{E}$, external electric field and $\mathit{B}$, external magnetic field) [Phys. Rev. Lett. 111, 246603 (2013)], where an enhancement factor proportional to $B^2$ is suggested to result from the $\mathit{E}·\mathit{B}$ term. In the present study, we show that this $B^2$ enhancement is not limited on the LMEC, where both the Seebeck and thermal conductivities in the longitudinal setup ($\mathit{E}\parallel \mathit{B}$) are predicted to show essentially the same enhancement proportional to $B^2$. In particular, the $B^2$ enhancement factor of the LMEC turns out to differ from that of the longitudinal thermal conductivity, responsible for the breakdown of the Wiedemann-Franz (WF) law, which means that anomalous currents flowing through the dissipationless channel differ from each other. Since the breakdown of the WF law appears in spite of the existence of electron quasiparticles, regarded to be a purely topological character (chiral anomaly), the Weyl metallic state cannot be identified with the Landau Fermi-liquid fixed point. We propose the violation of the WF law as another hallmark of the Weyl metallic phase, which originates from axion electrodynamics.

We present experimental results for the heavy-electron compound ${\mathrm{CeCu}}_4\mathrm{Ga}$ which show that it possesses short-range magnetic correlations down to a temperature of $T=0.1$ K. Our neutron scattering data show no evidence of long-range magnetic order occurring despite a peak in the specific heat at $T^{*}=1.2$ K. Rather, magnetic diffuse scattering occurs which corresponds to short-range magnetic correlations occurring across two unit cells. The specific heat remains large as $T\sim 0$ K, resulting in a Sommerfeld coefficient of ${\gamma }_0=1.44\left(2\right)$ J/mol ${\mathrm{K}}^2$, and, below $T^{*}$, the resistivity follows $T^2$ behavior and the ac magnetic susceptibility becomes temperature independent. A magnetic peak centered at an energy transfer of $E_{\mathrm{c}}=0.24\left(1\right)$ meV is seen in inelastic neutron scattering data which shifts to higher energies and broadens under a magnetic field. We discuss the coexistence of large specific heat, magnetic fluctuations, and short-range magnetic correlations at low temperatures and compare our results to those for materials possessing spin-liquid behavior.

A path integral approach is used to derive a closed analytical expression for the Kondo temperature of the SU(4) symmetrical Anderson model. In contrast to the SU(2) case, the prefactor of the Kondo temperature is found to display a peculiar orbital-energy (gate voltage) dependence, reflecting the presence of various SU(4) mixed valence fixed points. Our analytical expressions are tested against and confirmed by numerical renormalization group computations.

We develop a Gaussian variational approach in replica space to investigate the phase diagram of a one-dimensional interacting disordered topological superconducting wire in the strong-coupling regime. This method allows for a nonperturbative treatment in the disorder strength, electron-electron interactions, and the superconducting pairing amplitude. We find only two stable phases: a topological superconducting phase and a glassy, nontopological localized phase, characterized by replica symmetry breaking.

We present a systematic perturbative approach to study excitations in the thin cylinder/torus limit of the quantum Hall states. The approach is applied to the Haldane-Rezayi and Gaffnian quantum Hall states, which are both expected to have gapless excitations in the usual two-dimensional thermodynamic limit. For the Haldane-Rezayi state, we confirm that gapless excitations are present also in the “one-dimensional” thermodynamic limit of an infinite thin cylinder, in agreement with earlier considerations based on the wave functions alone. In contrast, we identify the lowest excitations of the Gaffnian state in the thin cylinder limit, and conclude that they are gapped, using a combination of perturbative and numerical means. We discuss possible scenarios for the crossover between the two-dimensional and the one-dimensional thermodynamic limit in this case.

Magnetic ratchets—two-dimensional systems with superimposed noncentrosymmetric ferromagnetic gratings—are considered theoretically. It is demonstrated that excitation by radiation results in a directed motion of two-dimensional carriers due to the pure orbital effect of the periodic magnetic field. Magnetic ratchets based on various two-dimensional systems such as topological insulators, graphene, and semiconductor heterostructures are investigated. The mechanisms of the electric current generation caused by both radiation-induced heating of carriers and by acceleration in the radiation electric field in the presence of a space-oscillating Lorentz force are studied in detail. The electric currents sensitive to the linear polarization plane orientation as well as to the radiation helicity are calculated. It is demonstrated that the frequency dependence of the magnetic ratchet currents is determined by the dominant elastic-scattering mechanism of two-dimensional carriers and differs for the systems with linear and parabolic energy dispersions.

The low-energy physics of silicene is described by Dirac fermions with a strong spin-orbit interaction and its band structure can be controlled by an external perpendicular electric field $E_z$. We investigate the commensurability oscillations in silicene modulated by a weak periodic potential $V=V_{0}cos(2\pi y/a_0)$ with $a_0$ as its period, in the presence of a perpendicular magnetic field $B$ and of a weak sinusoidal electric field $E_z=E_{0}cos(2\pi y/b_0)$, where $b_0$ is its period. We show that the spin and valley degeneracy of the Landau levels is lifted, due to the modulation, and that the interplay between the strong spin-orbit interaction and the potential and electric field modulations can result in spin- and valley-resolved magnetotransport. At very weak magnetic fields the commensurability oscillations induced by a weak potential modulation can exhibit a beating pattern depending on the strength of the homogenous electric field $E_z$ but this is not the case when only $E_z$ is modulated. The Hall conductivity plateaus acquire a step structure, due to spin and valley intra-Landau-level transitions, that is absent in unmodulated silicene. The results are critically contrasted with those for graphene and the two-dimensional electron gas.

Using first-principles density functional theory calculations, we investigate the hydrostatic pressure-induced reorientation of the Mn-F Jahn-Teller bond axis in the fluoride cryolite ${\mathrm{Na}}_3{\mathrm{MnF}}_6$. We find that a first-order isosymmetric phase transition (IPT) occurs between crystallographically equivalent monoclinic structures at approximately 2.15 GPa, consistent with earlier experimental studies. Mode-crystallography analyses of the pressure-dependent structures in the vicinity of the transition reveal a clear evolution of the Jahn-Teller bond distortions in cooperation with an asymmetrical stretching of the equatorial fluorine atoms in the ${\mathrm{MnF}}_6$ octahedral units. We identify a significant (70%) change in the orbital occupancy of the $e_g$ manifold of the $3d^4$ Mn(III) to be responsible for the transition, stabilizing one monoclinic $P{2}_1/n$ variant over the other. The orbital reconstruction as a driving force for the transition is confirmed by analogous calculations of isostructural $3d^0$ ${\mathrm{Na}}_3{\mathrm{ScF}}_6$, which shows no evidence of an IPT up to 6.82 GPa.

${\mathrm{Ba}}_{0.09}{\mathrm{Al}}_{0.18}{\mathrm{Ti}}_{0.12}{\mathrm{O}}_{0.61}$ glasses have been produced by aerodynamic levitation and laser heating. Neutron diffraction, x-ray diffraction, x-ray absorption spectroscopy, molecular dynamics simulation, and reverse Monte Carlo refinement methods have been used to obtain a detailed atomistic structural model of the glass. This model has been used to investigate its atomic coordination and network structure. It is found that the Al atoms are almost exclusively fourfold tetrahedrally coordinated to oxygen atoms. In contrast, the Ti atoms coordinate to oxygen atoms in approximately equal numbers of four- and fivefold coordinated sites with a small number of sixfold sites. The results show the presence of some tetrahedral ${\mathrm{TiO}}_4$ structural motifs although the dominant O-Ti-O bond angle occurs at ${90}^{\circ }$ . It is found that Al/Ti-O network structure shows strong similarities with other oxide glass forming systems although a first sharp diffraction peak is not observed. The results are used to discuss the unusual properties of the Ba-Al-Ti-O glasses produced under different quenching conditions.

Phase change or Ovonic memory technology has gained much interest in the past decade as a viable solution for the rapid increase in the demand for memory storage. This unique technology, first proposed by S. Ovshinsky in 1968, is based on storing information on the crystalline and amorphous phases of a material. The most common phase-change materials (PCMs) use chalcogenide alloys such as the ${\mathrm{Ge}}_2{\mathrm{Sb}}_2{\mathrm{Te}}_5$ (GST225). However, while the structure of its crystalline phase is relatively well characterized as consisting of a rhombohedrally distorted rock-salt lattice, the corresponding amorphous phase remains still poorly understood. Here, we show that ${}^{119}\mathrm{Sn}$ Mössbauer spectroscopy and angular constraint counting of simulated structures can provide a quantitative measure of the ${sp}^3$ tetrahedral fraction of Ge or Si cation in amorphous phase-change binary tellurides ${\mathrm{Ge}}_x{\mathrm{Te}}_{1-x}$ and ${\mathrm{Si}}_x{\mathrm{Te}}_{1-x}$. This represents the first quantitative estimate of such local structures, and reveals the fraction to be nearly 50%, while also revealing implications for the phase-change mechanism itself.

We numerically study the interplay between superconductivity and disorder on the graphene honeycomb lattice with on-site Hubbard attractive interactions $U$ using a spatially inhomogeneous self-consistent Bogoliubov–de Gennes (BdG) approach. In the absence of disorder there are two phases at charge neutrality. Below a critical value $U_c$ for attractive interactions there is a Dirac semimetal phase and above it there is a superconducting phase. We add scalar potential disorder to the system, while remaining at charge neutrality on average. Numerical solution of the BdG equations suggests that while in the strong attraction regime ($U>U_c$) disorder has the usual effect of suppressing superconductivity, in the weak attraction regime ($U<U_c$) weak disorder enhances superconductivity. In the weak attraction regime, disorder that is too strong eventually suppresses superconductivity, i.e., there is an optimal disorder strength that maximizes the critical temperature $T_c$. Our numerical results also suggest that in the weakly disordered regime, mesoscopic inhomogeneities enhance superconductivity significantly more than what is predicted by a spatially uniform mean-field theory in the manner of Abrikosov and Gorkov. In this regime, superconductivity consists of rare phase-coherent superconducting islands. We also study the enhancement of the superconducting proximity effect by disorder and mesoscopic inhomogeneities, and obtain typical spatial plots of the tunneling density of states and the superfluid susceptibility that can be directly compared to scanning tunneling microscopy experiments on proximity-induced superconductivity in graphene.

The charge transported when a quantum pump is adiabatically driven by time-dependent external forces in presence of dissipation is given by the line integral of a pumping field $\mathit{F}$. We give a general expression of $\mathit{F}$ in terms of quantum correlation functions evaluated at fixed external forces. Hence, an advantage of our method is that it transforms the original time-dependent problem into an autonomous one. Yet another advantage is that the curl of $\mathit{F}$ gives immediate visual information about the geometric structures governing dissipative quantum pumping. This can be used in a wide range of experimental cases, including electron pumps based on quantum dots and Cooper-pair pumps based on superconducting devices. Applied to a Cooper-pair sluice, we find an intriguing dissipation-induced enhancement of charge pumping, reversals of current, and emergence of asymmetries. This geometric method thus enables one to unveil a plethora of beneficial, dissipation-assisted operation protocols.

A recent theoretical proposal suggests that a simple circuit utilizing two superinductors may produce a qubit with ground-state degeneracy [Brooks, Phys. Rev. A 87, 052306 (2013)]. We perform a full circuit analysis along with exact diagonalization of the circuit Hamiltonian to elucidate the nature of the spectrum and low-lying wave functions of this $0\text{−}\pi$ device. We show that the ground-state degeneracy is robust to disorder in charge, flux, and critical current as well as insensitive to modest variations in the circuit parameters. Our treatment is nonperturbative, provides access to excited states and matrix elements, and is immediately applicable also to intermediate parameter regimes of experimental interest.

We introduce interatomic potentials for tungsten in the bcc crystal phase and its defects within the Gaussian approximation potential framework, fitted to a database of first-principles density functional theory calculations. We investigate the performance of a sequence of models based on databases of increasing coverage in configuration space and showcase our strategy of choosing representative small unit cells to train models that predict properties observable only using thousands of atoms. The most comprehensive model is then used to calculate properties of the screw dislocation, including its structure, the Peierls barrier and the energetics of the vacancy-dislocation interaction. All software and raw data are available at www.libatoms.org.

We present a model of classical Heisenberg spins on a hollandite lattice, which has been developed to describe the magnetic properties of $\alpha {\text{−}\mathrm{MnO}}_2$ and similar compounds. The model has only nearest-neighbor interacting spins, however, the strength and the sign of spin-spin interactions is anisotropic and depends on the nature of the bonds. Our analysis shows that the hollandite lattice supports four different incommensurate and helical magnetic ground states depending on the relative strengths and signs of spin-spin interactions. We show that the incommensurate helical ground states appear due to the geometrical frustration present in the model. We demonstrate that each of the four helical incommensurate magnetic phases are continuously connected to four different collinear antiferromagnetic ground states as the strength of spin-spin interaction along some bonds is increased. The present results give support to the presence of helical states that have been previously suggested experimentally for hollandite compounds. We provide an in-depth analysis of the magnetic form factors for each helical phase and describe how it could be used to identify each of these phases in neutron diffraction experiments.

The electrical resistivity, anisotropic magnetoresistance (AMR), and anomalous Hall effect of ferromagnetic ${\mathrm{Mn}}_5{\mathrm{Ge}}_3,{\mathrm{Mn}}_5{\mathrm{Ge}}_3{\mathrm{C}}_{0.8}$, and ${\mathrm{Mn}}_5{\mathrm{Si}}_3{\mathrm{C}}_{0.8}$ thin films has been investigated. The data show a behavior characteristic for a ferromagnetic metal, with a linear increase of the anomalous Hall coefficient with Curie temperature. While for ferromagnetic ${\mathrm{Mn}}_5{\mathrm{Si}}_3{\mathrm{C}}_{0.8}$ the normal Hall coefficient $R_0$ and the AMR ratio are independent of temperature, these parameters strongly increase with temperature for ${\mathrm{Mn}}_5{\mathrm{Ge}}_3{\mathrm{C}}_x$ films. This difference is presumably due to the different lattice parameters and different atomic configurations of the metalloids Ge and Si affecting the electronic band structure. The concomitant sign change of $R_0$ and the AMR ratio with temperature observed for ${\mathrm{Mn}}_5{\mathrm{Ge}}_3{\mathrm{C}}_x$ films is discussed in a two-current model indicating an electronlike minority-spin transport at low temperatures.

The magnetocaloric effect of a magnetic material is characterized by two quantities, the isothermal entropy change and the adiabatic temperature change, both of which are functions of temperature and applied magnetic field. We discuss the scaling properties of these quantities close to a second-order phase transition within the context of the theory of critical phenomena. Sufficiently close to the critical temperature of a second-order material, the scaling of the isothermal entropy change will be determined by the critical exponents and will be the same as that of the singular part of the entropy itself. However, this is only true in the critical region near $T_c$ and for small fields; for finite fields, scaling with constant exponents, in general, break down, even at $T_c$. The field dependence can then be described by field-dependent scaling exponents. We show that the scaling exponents at finite fields are not universal, showing significant variation for models in the same universality class. As regards the adiabatic temperature change, it is not determined exclusively by the singular part of the free energy and its derivatives. We show that the field dependence of the adiabatic temperature change at the critical temperature depends on the nonsingular part of the specific heat. The field dependence can still be fitted to a power-law expression but with nonuniversal exponents, as we show explicitly both within mean-field theory and using the so-called Arrott-Noakes equation of state. Within the framework of the Bean-Rodbell model, we briefly consider the scaling properties of the magnetocaloric effect in first-order materials. Finally, we discuss the implications of our findings for a widely used phenomenological scaling procedure for magnetocaloric quantities.

The transverse voltages generated in a ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$ ferromagnetic semiconductor in planar Hall effect and transverse spin Seebeck effect configurations are systematically analyzed. The observed field dependences consist of symmetric and asymmetric contributions. The former is attributed to the planar Nernst effect in the magnetic film in the presence of an in-plane temperature gradient, while the latter is caused by the anomalous Nernst effect due to spurious out-of-plane temperature gradients with a coefficient as high as 500 $\mu V/K$. We also report on the experimental observation of the planar Hall effect measured at different temperatures. Using a Stoner-Wohlfarth model for data analysis, the anisotropy constants $K_u$ and $K_c$ of superimposed uniaxial and cubic anisotropies in the magnetic film are determined. The temperature dependence of the $K_u/K_c$ ratio reveals a gradual substitution of the cubic anisotropy dominating at low temperatures with the uniaxial anisotropy as the temperature rises. This behavior is confirmed by the simultaneous domain observation using Kerr microscopy, demonstrating different field evolutions of the domain structure at different temperatures.