Weak antilocalization in HgTe quantum wells and topological surface states: Massive versus massless Dirac fermions

TL;DR

This paper compares weak antilocalization effects in HgTe quantum wells and topological insulator surface states, highlighting how a finite Dirac mass in HgTe influences quantum interference and magnetoconductivity.

Contribution

It provides a theoretical analysis of how finite Dirac mass suppresses weak antilocalization in HgTe quantum wells, contrasting with massless topological surface states.

Findings

Weak antilocalization is suppressed in HgTe quantum wells at long times due to a relaxation gap.

The relaxation gap depends nonmonotonically on carrier density and band gap.

Topological surface states show distinct magnetoconductivity behavior in parallel magnetic fields.

Abstract

HgTe quantum wells and surfaces of three-dimensional topological insulators support Dirac fermions with a single-valley band dispersion. In the presence of disorder they experience weak antilocalization, which has been observed in recent transport experiments. In this work we conduct a comparative theoretical study of the weak antilocalization in HgTe quantum wells and topological surface states. The difference between these two single-valley systems comes from a finite band gap (effective Dirac mass) in HgTe quantum wells in contrast to gapless (massless) surface states in topological insulators. The finite effective Dirac mass implies a broken internal symmetry, leading to suppression of the weak antilocalization in HgTe quantum wells at times larger than certain t_M, inversely proportional to the Dirac mass. This corresponds to the opening of a relaxation gap 1/t_M in the Cooperon diffusion mode which we obtain from the Bethe-Salpeter equation including relevant spin degrees of freedom. We demonstrate that the relaxation gap exhibits an interesting nonmonotonic dependence on both carrier density and band gap, vanishing at a certain combination of these parameters. The weak-antilocalization conductivity reflects this nonmonotonic behavior which is unique to HgTe QWs and absent for topological surface states. On the other hand, the topological surface states exhibit specific weak-antilocalization magnetoconductivity in a parallel magnetic field due to their exponential decay in the bulk.