Conductivity Corrections for Topological Insulators with Spin-Orbit Impurities: A New Hikami-Larkin-Nagaoka Formula

TL;DR

This paper derives a new formula for quantum conductivity corrections in 3D topological insulators with spin-orbit impurities, revealing universal weak antilocalization behavior and challenging previous experimental interpretations.

Contribution

It introduces a modified Hikami-Larkin-Nagaoka formula tailored for massless Dirac fermions in topological insulators, accounting for spin-orbit impurity effects.

Findings

Conductivity correction is always positive, indicating universal weak antilocalization.

The correction to the diffusion constant is linearly proportional to impurity spin-orbit strength.

Reinterpretation of experimental magnetoconductivity data using the new formula is necessary.

Abstract

The Hikami-Larkin-Nagaoka (HLN) formula [Prog. Theor. Phys. 63, 707 (1980)] describes the quantum corrections to the magnetoconductivity of a quasi-2D electron gas (quasi-2DEG) with parabolic dispersion. It predicts a crossover from weak localization to antilocalization as a function of the strength of scattering off spin-orbit impurities. Here, we derive the conductivity correction for massless Dirac fermions in 3D topological insulators (TIs) in the presence of spin-orbit impurities. We show that this correction is always positive and therefore we predict weak antilocalization for every value of the spin-orbit disorder. Furthermore, the correction to the diffusion constant is surprisingly linear in the strength of the impurity spin-orbit. Our results call for a reinterpretation of experimental fits for the magnetoconductivity of 3D TIs which have so far used the standard HLN formula.