Interfacial charge and spin transport inZ2topological insulators

Abstract

The Kane-Mele model realizes a two-dimensional version of a ${\mathbb{Z}}_{2}$ topological insulator as an idealized model of graphene with intrinsic and extrinsic (Rashba) spin-orbit couplings. We study the transport of charge and spin in such a Dirac electron system in the presence of a sharp potential step, that is, a $\mathit{pn}$ junction. An electron incident normal to the junction is completely reflected when Rashba coupling is dominant, whereas it is perfectly transmitted when the two types of couplings are balanced. The latter manifests in charge transport as a peak of conductance and a dip in Fano factor. Charge transport occurs in the direction normal to the barrier, whereas a spin current is induced along the barrier that is also localized in its vicinity. It is demonstrated that contributions from interband matrix elements and evanescent modes are responsible for such an interfacial spin Hall current. Our analysis of spin transport is based on the observation that in the case of vanishing Rashba coupling, each channel carries a conserved spin current, whereas only the integrated spin current is a conserved quantity in the general case. The perfect transmission/reflection of charge and conserved spin current is a consequence of reflection symmetry. Finally, we provide a quasiclassical picture of charge and spin transport by imaging flow lines over the entire sample and Veselago lensing (negative refraction).