Topological response theory of doped topological insulators

TL;DR

This paper extends the topological response theory to doped topological insulators, revealing an inhomogeneity-induced Berry phase contribution to surface Hall conductivity that depends solely on occupied states.

Contribution

It introduces a generalized response theory for doped TIs, accounting for finite bulk carriers and surface effects, and predicts measurable surface Hall conductivity behavior.

Findings

Surface Hall conductivity includes an inhomogeneity-induced Berry phase component.

In the zero bulk carrier limit, the conductivity matches the half-integer quantized value.

Predictions enable experimental verification in doped TI systems with gating.

Abstract

We generalize the topological response theory of three-dimensional topological insulators (TI) to metallic systems-specifically, doped TI with finite bulk carrier density and a time-reversal symmetry breaking field near the surface. We show that there is an inhomogeneity-induced Berry phase contribution to the surface Hall conductivity that is completely determined by the occupied states and is independent of other details such as band dispersion and impurities. In the limit of zero bulk carrier density, this intrinsic surface Hall conductivity reduces to the half-integer quantized surface Hall conductivity of TI. Based on our theory we predict the behavior of the surface Hall conductivity for a doped topological insulator with a top gate, which can be directly compared with experiments.