The quantum corrections to the conductivity and thermopower in monolayer graphene are studied. We use the recursive Green's-function method to calculate numerically the conductivity and thermopower of graphene. We then analyze these weak-localization corrections by fitting with the analytical theory as a function of the impurity parameters and gate potential. As a result of the quantum corrections to the thermopower, we find large magnetothermopower, which is shown to provide a very sensitive measure of the size and strength of the impurities. We compare these analytical and numerical results with existing experimental measurements of magnetoconductance of single-layer graphene and find that the average size and strength of the impurities in these samples can thereby be determined. We suggest favorable parameter ranges for future measurements of the magnetothermopower.

We study strained ${\text{Hg}}_{1-x-y}$${\text{Cd}}_x$${\text{Mn}}_y$Te in a magnetic field using a $\mathit{k}·\mathit{p}$ model and predict that the system is a Weyl semimetal with two nodes in an experimentally reasonable region of the phase diagram. We also predict two signatures of the Weyl semimetal phase which arise from tunability of the Weyl node splitting. First, we find that the Hall conductivity is proportional to the average Mn ion spin and thus is strongly temperature dependent. Second, we find an unusual magnetic field angle dependence of the Hall conductivity; in particular, we predict a peak in ${\sigma }_{xy}$ as a function of field angle in the $xz$ plane and a finite ${\sigma }_{yz}$ as the $x$ component of the field goes to zero.

We construct a lattice model for a cubic Kondo insulator consisting of one spin-degenerate $d$ and $f$ orbital at each lattice site. The odd-parity hybridization between the two orbitals permits us to obtain various trivial and topological insulating phases, which we classify in the presence of cubic symmetry. In particular, depending on the choice of our model parameters, we find a strong topological insulator phase with a band inversion at the $X$ point, modeling the situation potentially realized in ${\mathrm{SmB}}_6$, and a topological crystalline insulator phase with trivial ${\mathbb{Z}}_2$ indices but nonvanishing mirror Chern numbers. Using the Kotliar-Ruckenstein slave-boson scheme, we further demonstrate how increasing interactions among $f$ electrons can lead to topological phase transitions. Remarkably, for fixed band parameters, the $f$-orbital occupation number at the topological transitions is essentially independent of the interaction strength, thus yielding a robust criterion to discriminate between different phases.

In high-quality two-dimensional electrons confined to GaAs quantum wells, near Landau level filling factors $\nu =1/2$ and 1/4, we observe signatures of the commensurability of the electron-flux composite fermion cyclotron orbits with a unidirectional periodic density modulation. Focusing on the data near $\nu =1/2$, we directly and quantitatively probe the shape of the composite fermions' cyclotron orbit, and therefore their Fermi contour, as a function of magnetic field ($B_{\parallel }$) applied parallel to the sample plane. The composite fermion Fermi contour becomes severely distorted with increasing $B_{\parallel }$ and appears to be elliptical, in sharp contrast to the electron Fermi contour which splits as the system becomes bilayerlike at high $B_{\parallel }$. We present a simple, qualitative model to interpret our findings.

We develop a simple model of surface states for topological insulators, developing matching relations for states on surfaces of different orientations. The model allows one to write simple Dirac Hamiltonians for each surface, and to determine how perturbations that couple to electron spin impact them. We then study two specific realizations of such systems: quantum wires of rectangular cross-section and a rectangular slab in a magnetic field. In the former case, we find a gap at zero energy due to the finite size of the system. This can be removed by application of exchange fields on the top and bottom surfaces, which lead to gapless chiral states appearing on the lateral surfaces. In the presence of a magnetic field, we examine how Landau level states on surfaces perpendicular to the field join onto confined states of the lateral surfaces. We show that an imbalance in the number of states propagating in each direction on the lateral surface is sufficient to stabilize a quantized Hall effect if there are processes that equilibrate the distribution of current among these channels.

We study a heterostructure which consists of a topological insulator and a superconductor with a hole. The hole pins a vortex. The system supports a robust Majorana fermion state bound to the vortex core. We investigate the possibility of using scanning tunneling spectroscopy (i) to detect the Majorana fermion in the proposed setup and (ii) to study excited states bound to the vortex core. The Majorana fermion manifests itself as a magnetic-field-dependent zero-bias anomaly of the tunneling conductance. Optimal parameters for detecting Majorana fermions have been obtained. In the optimal regime, the Majorana fermion is separated from the excited states by a substantial gap. The number of zero-energy states equals the number of flux quanta in the hole; thus, the strength of the zero-bias anomaly depends on the magnetic field. The lowest energy excitations bound to the core are also studied. The excited states spectrum differs from the spectrum of a typical Abrikosov vortex, providing additional indirect confirmation of the Majorana state observation.

We study electron transport properties of composite ferroelectrics—materials consisting of metallic grains embedded in a ferroelectric matrix. In particular, we calculate the conductivity in a wide range of temperatures and electric fields, showing pronounced hysteretic behavior. In weak fields, electron cotunneling is the main transport mechanism. In this case, we show that the ferroelectric matrix strongly influences the transport properties through two effects: (i) the dependence of the Coulomb gap on the dielectric permittivity of the ferroelectric matrix, which in turn is controlled by temperature and external field, and (ii) the dependence of the tunneling matrix elements on the electric polarization of the ferroelectric matrix, which can be tuned by temperature and applied electric field as well. In the case of strong electric fields, the Coulomb gap is suppressed and only the second mechanism is important. Our results are important for (i) thermometers for precise temperature measurements and (ii) ferrroelectric memristors.

We show that there exist dynamical phase transitions (DPTs), as defined by Heyl et al. [Phys. Rev. Lett. 110, 135704 (2013)], in the transverse-field Ising model (TFIM) away from the static quantum critical points. We study a class of special states associated with singularities in the generating functions of time-integrated observables as found by Hickey et al. [Phys. Rev. B 87, 184303 (2013)]. Studying the dynamics of these special states under the evolution of the TFIM Hamiltonian, we find temporal nonanalyticities in the initial-state return probability associated with dynamical phase transitions. By calculating the Berry phase and Chern number we show the set of special states have interesting geometric features similar to those associated with static quantum critical points.

Crystal structure, magnetic, and transport properties of the ${\text{U}}_2$${\text{Fe}}_3$Ge compound have been studied under hydrostatic pressure. ${\text{U}}_2$${\text{Fe}}_3$Ge crystallizes in the hexagonal crystal structure of the ${\text{Mg}}_2$${\text{Cu}}_3$Si type, an ordered variant of the ${\text{MgZn}}_2$ Laves structure (C14). The Laves phase has proven highly stable; the crystal structure is maintained up to 27 GPa, the highest applied pressure. X-ray diffraction data revealed that the $c$ direction, where the shortest U-U bonds lie, is softer than the $a$ direction. The bulk modulus $B_0$ is ∼100 GPa. ${\text{U}}_2$${\text{Fe}}_3$Ge is an itinerant ferromagnet with the Curie temperature $T_{\mathrm{C}}$ = 55 K and the spontaneous magnetic moment $M_{\mathrm{s}}=1{\mu }_{\mathrm{B}}$ per formula unit at ambient pressure. The two parameters decrease rapidly under pressure with the rates $\mathrm{d}\left(\ln M_s\right)/\mathrm{d}p=-0.33$ GPa${}^{-1}$ and $\mathrm{d}\left(\ln T_{\mathrm{C}}\right)/\mathrm{d}p=-0.27$ GPa${}^{-1}$. The extrapolation of $T_{\mathrm{C}}$ and $M_{\mathrm{s}}$ indicates that the magnetic order will be suppressed between 3 and 4 GPa. Electrical resistivity was found to decrease gradually with increasing pressure. The data in the ferromagnetic state points to the opening of a gap in the magnon spectrum at higher pressures. ${\text{U}}_2$${\text{Fe}}_3$Ge is relatively more sensitive to pressure than isostructural ${\text{UNi}}_2$.

The magnetization reversal time of magnetic nanoparticles is investigated in the very low damping regime. The energy-controlled diffusion equation, rooted in a generalization of the Kramers escape rate theory for point Brownian particles in a potential to the magnetic relaxation of a macrospin, yields the reversal time in closed integral form. The latter is calculated for a nanomagnet with uniaxial anisotropy with a uniform field applied at an angle to the easy axis and for a nanomagnet with biaxial anisotropy with the field along the easy axis. The results completely agree with those yielded by independent numerical and asymptotic methods.

We have used a combination of resonant magnetic x-ray scattering and x-ray absorption spectroscopy to investigate the properties of the doped spin-orbital Mott insulator ${\mathrm{Sr}}_2$${\mathrm{Ir}}_{1-x}$${\mathrm{Rh}}_x$O${}_4$ ($0.07\le x\le 0.70$). We show that Sr${}_2$Ir${}_{1-x}$Rh${}_x$O${}_4$ represents a unique model system for the study of dilute magnetism in the presence of strong spin-orbit coupling, and provide evidence of a doping-induced change in magnetic structure and a suppression of magnetic order at $x_c\sim 0.17$. We demonstrate that Rh-doping introduces Rh${}^{3+}$/Ir${}^{5+}$ ions which effectively hole-dope this material. We propose that the magnetic phase diagram for this material can be understood in terms of a novel spin-orbital percolation picture.

We investigate the critical properties of cold bosonic gases in three dimensions, confined by an external quadratic potential coupled to the particle density, and realistically described by the Bose-Hubbard (BH) model. The trapping potential is often included in experiments with cold atoms and modifies the critical finite-size scaling of the homogeneous system in a nontrivial way. The trap-size scaling (TSS) theory accounts for this effect through the exponent $\theta$. We perform extensive simulations of the BH model at the critical temperature, in the presence of harmonic traps. We find that the TSS predictions are universal once we account for the effective way in which the trap locally modifies the chemical potential $\mu$ of the system. The trap exponent for the BH model at $\mu =0$ is the one corresponding to an effective quartic potential. At positive $\mu$, evidence suggests that TSS breaks down sufficiently far from the center of the trap, as the system encounters an effective phase boundary.

Laser-induced spin dynamics in (In,Mn)As is studied in magnetic fields up to 7 T. It is shown that a laser pulse can effectively excite homogenous spin precession in this compound at the frequency of the ferromagnetic resonance. Laser excitation of this resonance appears to be very ineffective if the applied magnetic field is below 1.5 T at 10 K. Our analysis shows that the damping of the laser-induced spin precession is a function of magnetic field and reaches very high values below 1.5 T.

We present molecular dynamics simulations using a Tersoff-like potential of single crystals of silicon shock compressed along the $\langle 001\rangle$ direction. We find an elastic response up to a critical stress, above which the shear stress is relieved by an inelastic response associated with a partial transformation to a new high-pressure phase, where both the new phase (Imma) and the original cubic diamond phase are under close to hydrostatic conditions. We study how the fraction of the two phases is related to both their geometry and their enthalpy, and discuss the relevance of the results to previous experimental measurements of the response of silicon to shock compression. We note that the simulations are consistent with shear stress relief provided directly by the shock-induced phase transition itself, without an intermediate state of plastic deformation of the cubic diamond phase, but that the onset of inelastic behavior within the simulations still occurs at considerably higher stresses than found in experiments.

Harmonic calculations based on density-functional theory are generally the method of choice for the description of phonon spectra of metals and insulators. The inclusion of anharmonic effects is, however, delicate as it relies on perturbation theory requiring a considerable amount of computer time, fast increasing with the cell size. Furthermore, perturbation theory breaks down when the harmonic solution is dynamically unstable or the anharmonic correction of the phonon energies is larger than the harmonic frequencies themselves. We present here a stochastic implementation of the self-consistent harmonic approximation valid to treat anharmonicity at any temperature in the nonperturbative regime. The method is based on the minimization of the free energy with respect to a trial density matrix described by an arbitrary harmonic Hamiltonian. The minimization is performed with respect to all the free parameters in the trial harmonic Hamiltonian, namely, equilibrium positions, phonon frequencies, and polarization vectors. The gradient of the free energy is calculated following a stochastic procedure. The method can be used to calculate thermodynamic properties, dynamical properties, and even anharmonic corrections to the Eliashberg function of the electron-phonon coupling. The scaling with the system size is greatly improved with respect to perturbation theory. The validity of the method is demonstrated in the strongly anharmonic palladium and platinum hydrides. In both cases, we predict a strong anharmonic correction to the harmonic phonon spectra, far beyond the perturbative limit. In palladium hydrides, we calculate thermodynamic properties beyond the quasiharmonic approximation, while in PtH, we demonstrate that the high superconducting critical temperatures at 100 GPa predicted in previous calculations based on the harmonic approximation are strongly suppressed when anharmonic effects are included.

A first-principles-based effective Hamiltonian is used to reveal dynamics of vortices in ferroelectrics. In addition to the “usual” dielectric modes that are generated by the fluctuation of the electrical polarization, additional toroidic modes, resulting from the electric toroidal moment fluctuations, are also found in the THz regime. Such latter modes can have their own dynamics, with a resonant frequency that softens via a square-root law when the temperature approaches the critical temperature at which electric vortices form. These dynamics are also found to be governed by the fluctuation of the self-organized azimuthal component of individual electric dipoles. Toroidic modes thus behave as pendulums, in contrast to springs that represent polarization dynamics.

We calculate the dielectric response of crystalline silicon following irradiation by a high-intensity laser pulse, modeling the dynamics by the time-dependent Kohn-Sham equations in the presence of the laser field. Pump-probe measurements of the response are numerically simulated by including both pump and probe externals fields in the simulation. As expected, the excited silicon shows features of an electron-hole plasma of nonequilibrium phase in its response, characterized by a negative divergence in the real part of the dielectric function at small frequencies. The response to the probe pulse depends on the polarization of the pump pulse. We also find that the imaginary part of the dielectric function can be negative, particularly for the parallel polarization of pump and probe fields. We compare the calculated response with a simple Drude model. The real part of the dielectric function is well fitted by the model, treating the effective mass as a fitting parameter while taking electron density from the calculation. The fitted effective masses are consistent with carrier-band dispersions.

We present a formulation of the so-called Fermi sea contribution to the conductivity tensor of spin-polarized random alloys within the fully relativistic tight-binding linear muffin-tin-orbital (TB-LMTO) method and the coherent potential approximation (CPA). We show that the configuration averaging of this contribution leads to the CPA-vertex corrections that are solely due to the energy dependence of the average single-particle propagators. Moreover, we prove that this contribution is indispensable for the invariance of the anomalous Hall conductivities with respect to the particular LMTO representation used in numerical implementation. Ab initio calculations for cubic ferromagnetic $3d$ transition metals (Fe, Co, Ni) and their random binary alloys (Ni-Fe, Fe-Si) indicate that the Fermi sea term is small against the dominating Fermi surface term. However, for more complicated structures and systems, such as hexagonal cobalt and selected ordered and disordered Co-based Heusler alloys, the Fermi sea term plays a significant role in the quantitative theory of the anomalous Hall effect.

Using superconducting quantum interference device magnetometry techniques, we have studied the change in magnetization versus applied ac electric field, i.e. the magnetoelectric (ME) susceptibility $dM/dE$, in the chiral-lattice ME insulator ${\text{Cu}}_2{\text{OSeO}}_3$. Measurements of the $dM/dE$ response provide a sensitive and efficient probe of the magnetic phase diagram, and we observe clearly distinct responses for the different magnetic phases, including the skyrmion lattice phase. By combining our results with theoretical calculation, we estimate quantitatively the ME coupling strength as $\lambda =$ 0.0146 meV/(V/nm) in the conical phase. Our study demonstrates the ME susceptibility to be a powerful, sensitive, and efficient technique for both characterizing and discovering new multiferroic materials and phases.