Quantum Hall Effect in Thin Films of Three-Dimensional Topological Insulators

We show that a thin film of a three-dimensional topological insulator (3DTI) with an exchange field is a realization of the famous Haldane model for quantum Hall effect (QHE) without Landau levels. The exchange field plays the role of staggered fluxes on the honeycomb lattice, and the hybridization gap of the surface states is equivalent to alternating on-site energies on the AB sublattices. A peculiar phase diagram for the QHE is predicted in 3DTI thin films under an applied magnetic field, which is quite different from that either in traditional QHE systems or in graphene.Comment: 4 pages, 4 figure

A topological look at the quantum spin Hall state

We propose a topological understanding of the quantum spin Hall state without considering any symmetries, and it follows from the gauge invariance that either the energy gap or the spin spectrum gap needs to close on the system edges, the former scenario generally resulting in counterpropagating gapless edge states. Based upon the Kane-Mele model with a uniform exchange field and a sublattice staggered confining potential near the sample boundaries, we demonstrate the existence of such gapless edge states and their robust properties in the presence of impurities. These gapless edge states are protected by the band topology alone, rather than any symmetries.Comment: 5 pages, 4 figure

Spin Hall Effect and Spin Transfer in Disordered Rashba Model

Based on numerical study of the Rashba model, we show that the spin Hall conductance remains finite in the presence of disorder up to a characteristic length scale, beyond which it vanishes exponentially with the system size. We further perform a Laughlin's gauge experiment numerically and find that all energy levels cannot cross each other during an adiabatic insertion of the flux in accordance with the general level-repulsion rule. It results in zero spin transfer between two edges of the sample as each state always evolves back after the insertion of one flux quantum, in contrast to the quantum Hall effect. It implies that the topological spin Hall effect vanishes with the turn-on of disorder.Comment: 4 pages, 4 figures final versio