Effect of Electron-electron Interaction on Surface Transport in Three-Dimensional Topological Insulators

TL;DR

This paper investigates how electron-electron interactions influence the surface resistivity of 3D topological insulators, revealing a shape-dependent $T^2$ resistivity term that appears only when the Fermi surface is concave.

Contribution

It demonstrates the presence of a universal scaling form for surface resistivity near the convex/concave Fermi surface transition in 3D topological insulators.

Findings

The $T^2$ resistivity term appears only in the concave Fermi surface regime.

Resistivity follows a universal scaling law near the convex/concave transition.

Fermi surface shape change due to hexagonal warping affects surface transport properties.

Abstract

We study the effect of electron-electron interaction on the surface resistivity of three-dimensional (3D) topological insulators. In the absence of umklapp scattering, the existence of the Fermi-liquid ($T^2$) term in resistivity of a two-dimensional (2D) metal depends on the Fermi surface geometry, in particular, on whether it is convex or concave. On doping, the Fermi surface of 2D metallic surface states in 3D topological insulators of the Bi$_2$Te$_3$ family changes its shape from convex to concave due to hexagonal warping, while still being too small to allow for umklapp scattering. We show that the $T^2$ term in the resistivity is present only in the concave regime and demonstrate that the resistivity obeys a universal scaling form valid for an arbitrary 2D Fermi surface near a convex/concave transition.