Spin-orbit scattering for localized electrons: Absence of negative magnetoconductance

Observation of Anderson localization in ultrathin films of three-dimensional topological insulators

Anderson localization, the absence of diffusive transport in disordered systems, has been manifested as hopping transport in numerous electronic systems, whereas in recently discovered topological insulators it has not been directly observed. Here, we report experimental demonstration of a crossover from diffusive transport in the weak antilocalization regime to variable range hopping transport in the Anderson localization regime with ultrathin (Bi_{1-x}Sb_{x})_{2}Te_{3} films. As disorder becomes stronger, negative magnetoconductivity due to the weak antilocalization is gradually suppressed, and eventually, positive magnetoconductivity emerges when the electron system becomes strongly localized. This work reveals the critical role of disorder in the quantum transport properties of ultrathin topological insulator films, in which theories have predicted rich physics related to topological phase transitions.

Strong quantum interference in strongly disordered bosonic insulators

We study the variable-range hopping of bosons in an array of sites with short-range interactions and a large characteristic coordination number. The latter leads to strong quantum interference phenomena yet allows for their analytical study. We develop a functional renormalization-group scheme that repeatedly eliminates high-energy sites properly renormalizing the tunneling between the low-energy ones. Using this approach we determine the temperature and magnetic field dependence of the hopping conductivity and find a large positive magnetoresistance. With increasing magnetic field the behavior of the conductivity crossovers from the Mott's law to an activational behavior with the activation gap proportional to the magnetic field.

New spin-orbit-induced universality class in the integer quantum Hall regime

Using heuristic arguments and numerical simulations it is argued that the critical exponent nu describing the localization length divergence at the integer quantum-Hall transition is modified in the presence of spin-orbit scattering with short-range correlations. The exponent is very close to nu=4/3, the percolation correlation length exponent, consistent with the prediction of a semiclassical argument. In addition, a band of weakly localized states is conjectured.