Interaction and disorder effects in 3D topological insulator thin films

TL;DR

This paper develops a theoretical framework for understanding how interactions and disorder affect the electrical transport in 3D topological insulator thin films, revealing non-monotonic temperature dependence and topological effects.

Contribution

It introduces a comprehensive renormalization group analysis of surface interactions and disorder, highlighting the relevance of intersurface interactions and topological responses in 3D topological insulator films.

Findings

Intersurface interactions are relevant and destabilize decoupled surface states.

The system exhibits a non-monotonic temperature dependence of conductivity.

At low temperatures, the system flows to a metallic fixed point with identical surface properties.

Abstract

A theory of combined interference and interaction effects on the diffusive transport properties of 3D topological insulator surface states is developed. We focus on a slab geometry (characteristic for most experiments) and show that interactions between the top and bottom surfaces are important at not too high temperatures. We treat the general case of different surfaces (different carrier densities, uncorrelated disorder, arbitrary dielectric environment, etc.). In order to access the low-energy behavior of the system we renormalize the interacting diffusive sigma model in the one loop approximation. It is shown that intersurface interaction is relevant in the renormalization group (RG) sense and the case of decoupled surfaces is therefore unstable. An analysis of the emerging RG flow yields a rather rich behavior. We discuss realistic experimental scenarios and predict a characteristic non-monotonic temperature dependence of the conductivity. In the infrared (low-temperature) limit, the systems flows into a metallic fixed point. At this point, even initially different surfaces have the same transport properties. Investigating topological effects, we present a local expression of the $\mathbb Z_2$ theta term in the sigma model by first deriving the Wess-Zumino-Witten theory for class DIII by means of non-abelian bosonization and then breaking the symmetry down to AII. This allows us to study a response of the system to an external electromagnetic field. Further, we discuss the difference between the system of Dirac fermions on the top and bottom surfaces of a topological insulator slab and its non-topological counterpart in a double-well structure with strong spin-orbit interaction.