Effect of Perturbative Hexagonal Warping on Quantum Capacitance in Ultra-Thin Topological Insulators

TL;DR

This paper investigates how perturbative hexagonal warping affects quantum capacitance and Hall coefficient in ultra-thin topological insulators, revealing small corrections that preserve key physical behaviors.

Contribution

It introduces a perturbative approach to analyze hexagonal warping effects on surface state properties in ultra-thin topological insulators.

Findings

Quantum capacitance shows SdH oscillations with reduced frequencies.

Average quantum capacitance decreases with increased warping.

Hall conductivity remains largely unaffected by warping.

Abstract

Ultra-thin 3D topological insulators provide a stage to study the surface physics of such materials by minimizing the bulk contribution. Further, the experimentally verified snowflake like structure of the Fermi surface leads to a hexagonal warping term, and this discourse examines it as a perturbation in the presence of a magnetic field. We find that there are corrections to both energy dispersion and eigenstates which in turn alter the density of states in the presence of a magnetic field. Both the quantum capacitance and the Hall coefficient are evaluated analytically and it is shown here that we recover their established forms along with small corrections which preserve the object of treating hexagonal warping perturbatively. In our approach, the established Hall conductivity expression develops several minute correction terms and thus its behavior remains largely unaffected due to warping. The zero-temperature quantum capacitance exhibits SdH oscillations with reduced frequencies, with a lowered average capacitance with increased warping of the Fermi surface, while maintaining the usual amplitudes.