We performed a scanning tunneling spectroscopy investigation of the electronic properties of the topological insulator Bi${}_2$Te${}_3$ in the energy range between $-200$ and +700 meV with respect to the Fermi level. For unoccupied states, tunneling into topological surface states dominates. Analysis of Fourier-transformed (FT) $dI/dU$ maps allowed us to obtain their energy dispersion relation and to visualize the breakdown of the linear dispersion relation typical of massless particles. For occupied states, no signature of scattering events involving surface states can be detected. FT $dI/dU$ maps reveal in this case two scattering vectors pointing along the $\overline{\Gamma }\overline{M}$ and $\overline{\Gamma }\overline{K}$ directions. Both are identified with scattering events within bulk states. Interestingly, vectors pointing along $\overline{\Gamma }\overline{K}$ which correspond to bulk backscattering events have a length longer than the minimum distance necessary to match opposite pockets on a constant energy cut. Comparison with calculated spin-resolved constant-energy cuts shows that this is a direct consequence of the chiral spin texture present in bulk states when their energy and momentum are close to the resonances of the spin-polarized topological surface states.

Recently, many numerical evidences of fractional Chern insulator, i.e., the fractional quantum Hall states on lattices, are proposed when a Chern band is partially filled. Some trial wave functions of fractional Chern insulators can be obtained by mapping the fractional quantum Hall wave functions defined in the continuum onto the lattice through the Wannier state representation [Phys. Rev. Lett. 107, 126803 (2011)] in which the single particle Landau orbits in the Landau levels are identified with the one-dimensional Wannier states of the Chern bands with Chern number $C=1$. However, this mapping generically breaks the lattice point group symmetry. In this paper we discuss a general approach of modifying the mapping to accommodate the lattice rotational symmetry. The wave functions constructed through this modified mapping should serve as better trial wave functions in the thermodynamical limit and on the rotationally invariant finite lattice. Also these wave functions will form a good basis for the construction of lattice symmetry preserving pseudopotential formalism for fractional Chern insulators. The focus of this paper shall be mainly on the $C_4$ rotational symmetry of square lattices. Similar analysis can be straightforwardly generalized to triangular or hexagonal lattices with $C_6$ symmetry. We also generalize the discussion to the lattice symmetry of fractional Chern insulators with high Chern number bands.

We present a theoretical study of dispersion of states that form the bulk band-gap edges in the three-dimensional topological insulator Bi${}_2$Te${}_3$. Within density functional theory, we analyze the effect of atomic positions varied within the error range of the available experimental data and approximation chosen for the exchange-correlation functional on the bulk band gap and k-space location of valence- and conduction-band extrema. For each set of the positions with different exchange-correlation functionals, we show how many-body corrections calculated within a one-shot $GW$ approach affect the mentioned characteristics of electronic structure of Bi${}_2$Te${}_3$. We thus also illustrate to what degree the one-shot $GW$ results are sensitive to the reference one-particle band structure in the case of bismuth telluride. We found that for this topological insulator the $GW$ corrections enlarge the fundamental band gap and for certain atomic positions and reference band structure bring its value in close agreement with experiment.

We present one-shot $GW$ calculations of the bulk electronic structure of the topological insulators Bi${}_2$Se${}_3$ and Bi${}_2$Te${}_3$ within the all-electron full-potential linearized augmented-plane-wave formalism. We compare three different ways of treating the spin-orbit interaction in calculating the quasiparticle energies: (i) The spin-orbit coupling (SOC) is already incorporated in the noninteracting system that serves as starting point for the quasiparticle correction. (ii) The SOC is added in a second-variation approach only after the quasiparticle calculation has been performed in the absence of SOC. We found that the approximate treatment (ii) yields most quasiparticle bands with reasonable accuracy but does fail in the important band-gap region, where the SOC gives rise to a band inversion relevant for the topological properties of these materials. For example, Bi${}_2$Se${}_3$ is just on the brink of becoming a trivial semiconductor within this approximate approach, while it maintains its topological properties in the case of the consistent treatment (i). Finally, we consider another approach (iii), in which the SOC is included in the Green function $G$ as in (i), but neglected in the calculation of the screened Coulomb potential $W$. This approach gives results in very good agreement with the full treatment (i), but with a smaller numerical effort. We conclude that, in the high-symmetry directions studied, bulk Bi${}_2$Se${}_3$ is a direct-gap and Bi${}_2$Te${}_3$ an indirect-gap semiconductor with band gaps of 0.20 and 0.19 eV, respectively.

We consider two helical liquids on opposite edges of a two-dimensional topological insulator, which are connected by one or several local tunnel junctions. In the presence of spatially inhomogeneous Rashba spin-orbit coupling, the spin of the helical edge states is momentum dependent, and this spin texture can be different on opposite edges. We demonstrate that this has a strong impact on the electron transport between the edges. In particular, in the case of many random tunnel contacts, the localization length depends strongly on the spin textures of the edge states.

The structural and electronic recovery pathways of a photoexcited ultrathin vanadium dioxide (VO${}_2$) film at nanosecond time scales have been studied using time-resolved x-ray diffraction and transient optical absorption techniques. The recovery pathways from the tetragonal metallic phase to the monoclinic insulating phase are highly dependent on the optical pump fluence. At pump fluences higher than the saturation fluence of 14.7 mJ/cm${}^2$, we observed a transient structural state with lattice parameter larger than that of the tetragonal phase, which is decoupled from the metal-to-insulator phase transition. Subsequently, the photoexcited VO${}_2$ film recovered to the ground state at characteristic times dependent upon the pump fluence as a result of heat transport from the film to the substrate. We present a procedure to measure the time-resolved film temperature by correlating photoexcited and temperature-dependent x-ray diffraction measurements. A thermal transport model that incorporates changes of the thermal parameters across the phase transition reproduces the observed recovery dynamics. The optical excitation and fast recovery of ultrathin VO${}_2$ films provides a practical method to reversibly switch between the monoclinic insulating and tetragonal metallic state at nanosecond time scales.

We study the square-lattice Bose-Hubbard model with bounded random on-site energies at zero temperature. Starting from a dual representation obtained from a strong-coupling expansion around the atomic limit, we employ a real-space block decimation scheme. This approach is nonperturbative in the disorder and enables us to study the renormalization-group flow of the induced random-mass distribution. In both insulating phases, the Mott insulator and the Bose glass, the average mass diverges, signaling short range superfluid correlations. The relative variance of the mass distribution distinguishes the two phases, renormalizing to zero in the Mott insulator and diverging in the Bose glass. Negative mass values in the tail of the distribution indicate the presence of rare superfluid regions in the Bose glass. The breakdown of self-averaging is evidenced by the divergent relative variance and increasingly non-Gaussian distributions. We determine an explicit phase boundary between the Mott insulator and Bose glass.

It is argued that the anomalous Hall conductivity of ferromagnetic systems is fully determined by the response of the orbital momentum given by the so-called free electron currents to the gradient of the electrochemical potential. It is shown that for perfect Bloch systems it coincides with the well-known expression in which the conductivity is expressed in terms of the Berry phase curvature. The effect of the side-jump and skew scattering is discussed as well as the relation to the general form of the Kubo Hall-conductivity formula.

The ground-state magnetic properties of Co${}_x$Rh${}_{1-x}$ nanoparticles having sizes in the range of 0.8–2 nm ($N=43$ and 273 atoms) and Co concentrations $x\approx 0$, $0.25$, $0.5$, $0.75$, and 1 are investigated in the framework of density-functional theory by using a fixed-moment method. Electron correlation effects are explored by comparing the results of the local spin-density and generalized-gradient approximations to the exchange and correlation functional. The role of chemical order on the magnetic behavior is investigated by considering a variety of core-shell atomic arrangements with nearly spherical CoRh interfaces. A local relaxation of the cluster geometry is performed by taking face-centered cubic structures as starting configurations. All considered Co${}_x$Rh${}_{1-x}$ clusters are found to be magnetic with an average spin moment per CoRh unit that is larger than in macroscopic alloys having similar concentrations. This is a consequence of both, the enhancement of the Co moments and the occurrence of important induced Rh moments, which couple parallel to the Co moments. The distribution of the local magnetic moments within the clusters is found to depend strongly on the local and chemical environment of the atoms. In particular, the Rh moments show a nontrivial dependence as a function of the distance to the CoRh interface. The results for the local magnetic moments are correlated to the electronic densities of states, which reflect the concentration and chemical-order dependence of the cluster electronic structure. Finally, the effects of coating and of the 3$d$-4$d$ interface are analyzed by comparing the magnetic behaviors of core-shell particles with those of the corresponding pure Co and Rh cores.

The ensemble of spatially disordered and randomly oriented spherical monodispersed single-domain magnetic nanoparticles with cubic anisotropy was studied by the Monte Carlo method. In the presence of dipole-dipole interactions, the effect of both particle volume and interparticle separation was investigated with respect to the characteristic parameters of hysteresis loops and zero field cooled and field cooled magnetization curves. The coercive field and remanent magnetic moment were shown to depend strongly on the dimensionless parameter $\beta =k_{B}T/\left(K_{1}V\right)$ ($T$ temperature, $V$ particle volume, $K_1$ cubic anisotropy constant). It was revealed that strong dipole-dipole interactions suppress both the coercive field and the remanent magnetic moment of densely packed nanoparticles. Yet, the effect quickly diminishes with the increasing interparticle distances and becomes rather insignificant for separations exceeding three particle diameters. The blocking temperature was found to be weakly affected by dipolar interactions, but mainly governed via $\beta$, i.e., by the nanoparticle volume and the strength of crystalline anisotropy. The role of dipole-dipole interactions on magnetic properties of nanoparticles was further elucidated by a comparison of the simulation results for a single cluster with an infinite periodic arrangement of such clusters.

Na${}_2$Ti${}_2$$X_2$O ($X$ $=$ As, Sb) crystals have been grown from the flux method. X-ray diffraction characterization revealed an anti-K${}_2$NiF${}_4$-type layered structure (tetragonal, space group $I$4/mmm) for both compounds. Magnetic susceptibility $(\chi \left(T\right))$ and electrical resistivity (ρ$(T))$ measurements revealed major kinks at ∼115 K ($T_{\mathrm{s}1}$) and ∼320 K ($T_{\mathrm{s}2}$) for Na${}_2$Ti${}_2$Sb${}_2$O and Na${}_2$Ti${}_2$As${}_2$O, respectively, signifying possibly the opening of density wave gaps. Both Na${}_2$Ti${}_2$Sb${}_2$O and Na${}_2$Ti${}_2$As${}_2$O showed remarkably strong anisotropy in their electromagnetic transport properties, and values of ${\gamma }_{\rho }$ (${\rho }_{\mathrm{c}}/{\rho }_{\mathrm{ab}}$) even reached ∼140 and ∼430, respectively, being much larger than that of iron pnictide BaFe${}_2$As${}_2$ (${\gamma }_{\rho }$ ∼ 2–5). The ${\gamma }_{\rho }$ of Na${}_2$Ti${}_2$Sb${}_2$O changed slightly with cooling, though a small drop at $T_{\mathrm{s}1}$ occurred. In contrast, the ${\gamma }_{\rho }$ of Na${}_2$Ti${}_2$As${}_2$O changed strikingly by exhibiting not only a small change at $T_{\mathrm{s}2}$ but also a sudden decrease of ∼50 K, reduced nearly $1/3$. Specific heat measurement indicated that Na${}_2$Ti${}_2$Sb${}_2$O was only partially gapped with ${\gamma }_1$ $=$ 4.1 mJ mol${}^{-1}$ K${}^{-2}$, though a long-range order was established at $T{s}_1$, while Na${}_2$Ti${}_2$As${}_2$O was fully gapped. The remarkably strong electromagnetic anisotropy revealed in Na${}_2$Ti${}_2$$X_2$O suggests the crucial role of the TiO${}_2{X}_4$ layer for the transport properties of layered titanium oxypnictides.

The stress caused by vortices in tetragonal superconductors contributes to the intervortex interaction which depends on vortex orientation within the crystal, on elastic moduli, and is attractive within certain angular regions even in fields along the $c$ crystal axis. For sufficiently strong stress dependence of the critical temperature, this contribution may result in distortions of the hexagonal vortex lattice for $\mathit{H}\left|\right|\mathit{c}$. In small fields it leads to formation of a square vortex lattice with a fixed $H$ independent spacing. This should be seen in the magnetization $M\left(H\right)$ as a discontinuous jump of magnetization at the transition from the Meissner to mixed states.

The magnetic moment per Co${}^{4+}$ of $P2$($\gamma$)-type Na${}_x$CoO${}_2$ in the Curie-Weiss metal regime is revisited and examined under a proposed modification of the octahedral crystal electric field (CEF). The proposed model explains the origin of the existence of the intermediate state $S=1$ for Co${}^{3+}$ through an exciton-like elementary excitation of the narrow gap between the split $e_g$ and $t_{2g}$ groups. The CoO${}_2$ layer is proposed to be constructed from the tilted edge-sharing square-planar CoO${}_2$ chains with interchain coupling. The square-planar CEF of CoO${}_2$ requires covalent bond formation between Co and the four in-plane neighboring oxygens, while the oxygens sitting in the neighboring chains can be viewed as apical oxygens of low effective charge for a CoO${}_6$ pseudo-octahedron. The reason why angle-resolved photoemission spectroscopy failed to observe the local-density approximation (LDA) predicted $e_g^{\prime }$ hole pockets at $k_z=0$ and the reversed order of the $t_{2g}$ splittings between LDA and CEF calculations can also be resolved using the proposed model.

Submonolayer homoepitaxial fcc (110) systems display behavior reflecting strong anisotropy at lower temperatures, including one-dimensional decay during Ostwald ripening of rectangular islands maintaining constant width in the $\langle 001\rangle$ direction. To appropriately describe this behavior, we first develop a refined continuum Burton-Cabrera-Frank formalism, which accounts for a lack of equilibration of island shape and importantly also for inhibited incorporation of adatoms at almost-faceted $\langle \overline{1}10\rangle$ island edges through effective kinetic coefficients. This formalism is shown to describe accurately the adatom diffusion fluxes between islands and thus island evolution for a complex experimental island configuration, as confirmed by matching results from realistic atomistic simulations for this configuration. This approach also elucidates basic dependencies of flux on island geometry and temperature. Second, a further refinement is presented incorporating separate terrace and edge adatom density fields either in a continuum setting or alternatively in a spatially discrete diffusion equation setting. The second approach allows more flexibility and accuracy in accounting for edge-diffusion kinetics including corner rounding, a lack of equilibration of the edge adatom density at $\langle \overline{1}10\rangle$ island edges, and the effect of rare kinks on $\langle \overline{1}10\rangle$ island edges. Significantly, it suggests facile two-way corner rounding at the island periphery during island decay, contrasting the previous picture.

Localization of electrons in the two-dimensional electron gas at the LaAlO${}_3$/SrTiO${}_3$ interface is investigated by varying the channel thickness in order to establish the nature of the conducting channel. Layers of SrTiO${}_3$ were grown on NdGaO${}_3$ (110) substrates and capped with LaAlO${}_3$. When the SrTiO${}_3$ thickness is ≤6 unit cells, most electrons at the interface are localized, but when the number of SrTiO${}_3$ layers is 8–16, the free carrier density approaches 3.3×10${}^{14}$ cm${}^{-2}$, the value corresponding to charge transfer of 0.5 electrons per unit cell at the interface. The number of delocalized electrons decreases again when the SrTiO${}_3$ thickness is ≥20 unit cells. The ∼4 nm conducting channel is therefore located significantly below the interface. The results are explained in terms of Anderson localization and the position of the mobility edge with respect to the Fermi level.

To elucidate an origin of the two energy gaps in the narrow-gap semiconductor FeSb${}_2$, we have investigated the effects of hydrostatic pressure on the resistivity, Hall resistance, and magnetoresistance at low temperatures. The larger energy gap evaluated from the temperature dependence of resistivity above 100 K is enhanced from 30 to 40 meV with pressure from 0 to 1.8 GPa, as generally observed in conventional semiconductors. In the low-temperature range where a large Seebeck coefficient was observed, we evaluate the smaller energy gap from the magnetotransport tensor using a two-carrier model and find that the smaller gap exhibits a weak pressure dependence in contrast to that of the larger gap. To explain the pressure variations of the energy gaps, we propose a simple model that the smaller gap is a gap from the impurity level to the conduction band and the larger one is a gap between the valence and conduction bands, suggesting that the observed large Seebeck coefficient is not relevant to electron correlation effects.

We attract attention to the fact that the ultimate (shot-noise-limited) polarimetric sensitivity can be enhanced by orders of magnitude leaving the photon flux incident onto the photodetector on the same low level. This opportunity is of crucial importance for present-day spin noise spectroscopy, where a direct increase of sensitivity by increasing the probe beam power is strongly restricted by the admissible input power of the broadband photodetectors. The gain in sensitivity is achieved by replacing the 45${}^{\circ }$ polarization geometry commonly used in conventional schemes with balanced detectors by geometries with stronger polarization extinction. The efficiency of these high-extinction polarization geometries with enhancement of the detected signal by more than an order of magnitude is demonstrated by measurements of the spin noise spectra of bulk $n$:GaAs in the spectral range 835–918 nm. It is shown that the inevitable growth of the probe beam power with the sensitivity gain makes spin noise spectroscopy much more perturbative, but, at the same time, opens up fresh opportunities for studying nonlinear interactions of strong light fields with spin ensembles.

Amorphous to crystalline phase transitions in phase change materials (PCM) can have strong influence on the actuation of microelectromechanical systems under the influence of Casimir forces. Indeed, the bifurcation curves of the stationary equilibrium points and the corresponding phase portraits of the actuation dynamics between gold and AIST (Ag${}_5$In${}_5$Sb${}_{60}$Te${}_{30}$) PCM, where an increase of the Casimir force of up ∼25$\%$ has been measured upon crystallization, show strong sensitivity to changes of the Casimir force as the stiffness of the actuating component decreases and/or the effective interaction area of the Casimir force increases, which can also lead to stiction. However, introduction of intrinsic energy dissipation (associated with a finite quality factor of the actuating system) can prevent stiction by driving the system to attenuated motion towards stable equilibrium depending on the PCM state and the system quality factor.

The atomic structure of the supercooled liquid has often been discussed as a key source of glass formation in metals. The presence of icosahedrally coordinated clusters and their tendency to form networks have been identified as one possible structural trait leading to glass-forming ability in the Cu-Zr binary system. In this paper, we show that this theory is insufficient to explain glass formation at all compositions in that binary system. Instead, we propose that the formation of ideally packed clusters at the expense of atomic arrangements with excess or deficient free volume can explain glass forming by a similar mechanism. We show that this behavior is reflected in the structural relaxation of a metallic glass during constant pressure cooling and the time evolution of structure at a constant volume. We then demonstrate that this theory is sufficient to explain slowed diffusivity in compositions across the range of Cu-Zr metallic glasses.

Saturation field entropies of antiferromagnetic Ising models on quasi-one-dimensional lattices (ladders) and the kagome lattice are calculated. The former is evaluated exactly by constructing the corresponding transfer matrices, while the latter calculation uses Binder's algorithm for efficiently and exactly computing the partition function of over 1300 spins to give $S_{\mathrm{kag}}/k_B=0.393589\left(6\right)$. We comment on the relation of the kagome lattice to the experimental situation in the spin-ice compound Dy${}_2$Ti${}_2$O${}_7$.