Bott periodicity for the topological classification of gapped states of matter with reflection symmetry

Using a dimensional reduction scheme based on scattering theory, we show that the classification tables for topological insulators and superconductors with reflection symmetry can be organized in two period-two and four period-eight cycles, similar to the Bott periodicity found for topological insulators and superconductors without spatial symmetries. With the help of the dimensional reduction scheme the classification in arbitrary dimensions $d \ge 1$ can be obtained from the classification in one dimension, for which we present a derivation based on relative homotopy groups and exact sequences to classify one-dimensional insulators and superconductors with reflection symmetry. The resulting classification is fully consistent with a comprehensive classification obtained recently by Shiozaki and Sato [Phys.\ Rev.\ B {\bf 90}, 165114 (2014)]. The use of a scattering-matrix inspired method allows us to address the second descendant \bZ_2 phase, for which the topological nontrivial phase was previously reported to be vulnerable to perturbations that break translation symmetry.Comment: 18 pages, 7 figure

Tunable Magnetic Relaxation In Magnetic Nanoparticles

We investigate the magnetization dynamics of a conducting magnetic nanoparticle weakly coupled to source and drain electrodes, under the assumption that all relaxation comes from exchange of electrons with the electrodes. The magnetization dynamics is characterized by a relaxation time $t_1$, which strongly depends on temperature, bias voltage, and gate voltage. While a direct measure of a nanoparticle magnetization might be difficult, we find that $t_1$ can be determined through a time resolved transport measurement. For a suitable choice of gate voltage and bias voltage, the magnetization performs a bias-driven Brownian motion regardless of the presence of anisotropy.Comment: 4 pages, 2 eps figure

Mesoscopic effects in adiabatic spin pumping

We show that temporal shape modulations (pumping) of a quantum dot in the presence of spin-orbital coupling lead to a finite dc spin current. Depending on the strength of the spin-orbit coupling, the spin current is polarized perpendicular to the plane of the two-dimensional electron gas, or has an arbitrary direction subject to mesoscopic fluctuations. We analyze the statistics of the spin and charge currents in the adiabatic limit for the full cross-over from weak to strong spin-orbit coupling.Comment: 4 pages, 1 figure same as version 1. Added a comma to separate the two author name

Semiclassical theory of persistent current fluctuations in ballistic chaotic rings

The persistent current in a mesoscopic ring has a Gaussian distribution with small non-Gaussian corrections. Here we report a semiclassical calculation of the leading non-Gaussian correction, which is described by the three-point correlation function. The semiclassical approach is applicable to systems in which the electron dynamics is ballistic and chaotic, and includes the dependence on the Ehrenfest time. At small but finite Ehrenfest times, the non-Gaussian fluctuations are enhanced with respect to the limit of zero Ehrenfest time.Comment: 9 pages, 3 figures; submitted as invited contribution to a special issue in Physica E in memory of Markus Buettike

Semiclassical theory of speckle correlations

Coherent wave propagation in random media results in a characteristic speckle pattern, with spatial intensity correlations with short-range and long-range behavior. Here, we show how the speckle correlation function can be obtained from a ray picture for two representative geometries: A chaotic cavity and a random waveguide. Our calculation allows us to study the crossover between a "ray limit" and a "wave limit", in which the Ehrenfest time $\tau_E$ is larger or smaller than the typical transmission time $\tau_D$, respectively. Remarkably, long-range speckle correlations persist in the ray limit $\tau_E \gg \tau_D$.Comment: 13 pages, 7 figure

Density of states as a probe of electrostatic confinement in graphene

We theoretically analyze the possibility to confine electrons in single-layer graphene with the help of metallic gates, via the evaluation of the density of states of such a gate-defined quantum dot in the presence of a ring-shaped metallic contact. The possibility to electrostatically confine electrons in a gate-defined ``quantum dot'' with finite-carrier density, surrounded by an undoped graphene sheet, strongly depends on the integrability of the electron dynamics in the quantum dot. With the present calculations we can quantitatively compare confinement in dots with integrable and chaotic dynamics, and verify the prediction that the Berry phase associated with the pseudospin leads to partial confinement in situations where no confinement is expected according to the arguments relying on the classical dynamics only.Comment: 9 pages, 7 figure