Topological Effects on the Magnetoconductivity in Topological Insulators

TL;DR

This paper investigates how the topological nature of 3D topological insulators affects their magnetoconductivity, revealing effects of sidewall conduction, tilted fields, and a novel wrapped regime at low temperatures.

Contribution

It provides analytical and numerical insights into the topological effects on magnetoconductivity, including the impact of sidewalls and the prediction of a wrapped regime at low temperatures.

Findings

Sidewall conduction reduces magnetoconductivity systematically.

Tilted-field magnetoconductivity formulas match experimental measurements.

A wrapped regime emerges at low temperatures, altering temperature dependence.

Abstract

Three-dimensional strong topological insulators (TIs) guarantee the existence of a 2-D conducting surface state which completely covers the surface of the TI. The TI surface state necessarily wraps around the TI's top, bottom, and two sidewalls, and is therefore topologically distinct from ordinary 2-D electron gases (2DEGs) which are planar. This has several consequences for the magnetoconductivity $\Delta \sigma$, a frequently studied measure of weak antilocalization which is sensitive to the quantum coherence time $\tau_\phi$ and to temperature. We show that conduction on the TI sidewalls systematically reduces $\Delta \sigma$, multiplying it by a factor which is always less than one and decreases in thicker samples. In addition, we present both an analytical formula and numerical results for the tilted-field magnetoconductivity which has been measured in several experiments. Lastly, we predict that as the temperature is reduced $\Delta \sigma$ will enter a wrapped regime where it is sensitive to diffusion processes which make one or more circuits around the TI. In this wrapped regime the magnetoconductivity's dependence on temperature, typically $1/T^2$ in 2DEGs, disappears. We present numerical and analytical predictions for the wrapped regime at both small and large field strengths. The wrapped regime and topological signatures discussed here should be visible in the same samples and at the same temperatures where the Altshuler-Aronov-Spivak (AAS) effect has already been observed, when the measurements are repeated with the magnetic field pointed perpendicularly to the TI's top face.