Spin-orbit scattering in quantum diffusion of massive Dirac fermions

Effect of spin-orbit scattering on quantum diffusive transport of two-dimensional massive Dirac fermions is studied by the diagrammatic technique. The quantum diffusion of massive Dirac fermions can be viewed as a singlet Cooperon in the massless limit and a triplet Cooperon in the large-mass limit. The spin-orbit scattering behaves like random magnetic fields only to the triplet Cooperon, and suppresses the weak localization of Dirac fermions in the large-mass regime. This behavior suggests an experiment to detect the weak localization of bulk subbands in topological insulator thin films, in which a narrowing of the cusp of the negative magnetoconductivity is expected after doping heavy-element impurities. Finally, a detailed comparison between the conventional two-dimensional electrons and Dirac fermions is presented for impurities of orthogonal, symplectic, and unitary symmetries.Comment: 5 pages, 3 figures, 2 tables. To be submitted, comments are welcom

Coherent quantum transport in disordered systems I: The influence of dephasing on the transport properties and absorption spectra on one-dimensional systems

Excitonic transport in static disordered one dimensional systems is studied in the presence of thermal fluctuations that are described by the Haken-Strobl-Reineker model. For short times, non-diffusive behavior is observed that can be characterized as the free-particle dynamics in the Anderson localized system. Over longer time scales, the environment-induced dephasing is sufficient to overcome the Anderson localization caused by the disorder and allow for transport to occur which is always seen to be diffusive. In the limiting regimes of weak and strong dephasing quantum master equations are developed, and their respective scaling relations imply the existence of a maximum in the diffusion constant as a function of the dephasing rate that is confirmed numerically. In the weak dephasing regime, it is demonstrated that the diffusion constant is proportional to the square of the localization length which leads to a significant enhancement of the transport rate over the classical prediction. Finally, the influence of noise and disorder on the absorption spectrum is presented and its relationship to the transport properties is discussed.Comment: 23 pages, 7 figure

Loss of quantum coherence in a system coupled to a zero-temperature environment

We discuss the influence of a zero-temperature environment on a coherent quantum system. First, we calculate the reduced density operator of the system in the framework of the well-known, exactly solvable model of an oscillator coupled to a bath of harmonic oscillators. Then, we propose the sketch of an Aharonov--Bohm-like interferometer showing, through interference measurements, the decrease of the coherence length of the system due to the interaction with the environment, even in the zero temperature limit

Phase-coherent transport in catalyst-free vapor phase deposited Bi2_2Se3_3 crystals

Free-standing Bi$_2$Se$_3$ single crystal flakes of variable thickness are grown using a catalyst-free vapor-solid synthesis and are subsequently transferred onto a clean Si$^{++}$/SiO$_2$ substrate where the flakes are contacted in Hall bar geometry. Low temperature magneto-resistance measurements are presented which show a linear magneto-resistance for high magnetic fields and weak anti-localization (WAL) at low fields. Despite an overall strong charge carrier tunability for thinner devices, we find that electron transport is dominated by bulk contributions for all devices. Phase coherence lengths \l_\phi as extracted from WAL measurements increase linearly with increasing electron density exceeding $1 \mu$m at 1.7 K. While \l_\phi is in qualitative agreement with electron electron interaction-induced dephasing, we find that spin flip scattering processes limit \l_\phi at low temperatures.Comment: 8 pages, 5 figure

Functionals of the Brownian motion, localization and metric graphs

We review several results related to the problem of a quantum particle in a random environment. In an introductory part, we recall how several functionals of the Brownian motion arise in the study of electronic transport in weakly disordered metals (weak localization). Two aspects of the physics of the one-dimensional strong localization are reviewed : some properties of the scattering by a random potential (time delay distribution) and a study of the spectrum of a random potential on a bounded domain (the extreme value statistics of the eigenvalues). Then we mention several results concerning the diffusion on graphs, and more generally the spectral properties of the Schr\"odinger operator on graphs. The interest of spectral determinants as generating functions characterizing the diffusion on graphs is illustrated. Finally, we consider a two-dimensional model of a charged particle coupled to the random magnetic field due to magnetic vortices. We recall the connection between spectral properties of this model and winding functionals of the planar Brownian motion.Comment: Review article. 50 pages, 21 eps figures. Version 2: section 5.5 and conclusion added. Several references adde

Disorder and interference: localization phenomena

The specific problem we address in these lectures is the problem of transport and localization in disordered systems, when interference is present, as characteristic for waves, with a focus on realizations with ultracold atoms.Comment: Notes of a lecture delivered at the Les Houches School of Physics on "Ultracold gases and quantum information" 2009 in Singapore. v3: corrected mistakes, improved script for numerics, Chapter 9 in "Les Houches 2009 - Session XCI: Ultracold Gases and Quantum Information" edited by C. Miniatura et al. (Oxford University Press, 2011

Quantum oscillations and decoherence due to electron-electron interaction in metallic networks and hollow cylinders

We have studied the quantum oscillations of the conductance for arrays of connected mesoscopic metallic rings, in the presence of an external magnetic field. Several geometries have been considered: a linear array of rings connected with short or long wires compared to the phase coherence length, square networks and hollow cylinders. Compared to the well-known case of the isolated ring, we show that for connected rings, the winding of the Brownian trajectories around the rings is modified, leading to a different harmonics content of the quantum oscillations. We relate this harmonics content to the distribution of winding numbers. We consider the limits where coherence length $L_\varphi$ is small or large compared to the perimeter $L$ of each ring constituting the network. In the latter case, the coherent diffusive trajectories explore a region larger than $L$, whence a network dependent harmonics content. Our analysis is based on the calculation of the spectral determinant of the diffusion equation for which we have a simple expression on any network. It is also based on the hypothesis that the time dependence of the dephasing between diffusive trajectories can be described by an exponential decay with a single characteristic time $\tau_\varphi$ (model A) . At low temperature, decoherence is limited by electron-electron interaction, and can be modelled in a one-electron picture by the fluctuating electric field created by other electrons (model B). It is described by a functional of the trajectories and thus the dependence on geometry is crucial. Expressions for the magnetoconductance oscillations are derived within this model and compared to the results of model A. It is shown that they involve several temperature-dependent length scales.Comment: 35 pages, revtex4, 25 figures (34 pdf files

Spin dynamics in semiconductors

This article reviews the current status of spin dynamics in semiconductors which has achieved a lot of progress in the past years due to the fast growing field of semiconductor spintronics. The primary focus is the theoretical and experimental developments of spin relaxation and dephasing in both spin precession in time domain and spin diffusion and transport in spacial domain. A fully microscopic many-body investigation on spin dynamics based on the kinetic spin Bloch equation approach is reviewed comprehensively.Comment: a review article with 193 pages and 1103 references. To be published in Physics Reports