Surface states in a 3D topological insulator: The role of hexagonal warping and curvature

TL;DR

This paper investigates how hexagonal warping and finite effective mass influence the electronic states and Landau levels in 3D topological insulators, revealing singularities and modifications in Landau level evolution.

Contribution

It provides a detailed analysis of the combined effects of warping and curvature on TDOS and Landau levels, including experimental verification and theoretical predictions.

Findings

Warpage transforms van Hove singularity into a logarithmic one.

Additional singularities and TDOS jumps are observed at moderate warping.

Landau levels are significantly altered due to degeneracy removal.

Abstract

We explore a combined effect of hexagonal warping and of finite effective mass on both the tunneling density of electronic states (TDOS) and structure of Landau levels (LLs) of 3D topological insulators. We find the increasing warping to transform the square-root van Hove singularity into a logarithmic one. For moderate warping an additional logarithmic singularity and a jump in the TDOS appear. This phenomenon is experimentally verified by direct measurements of the local TDOS in Bi$_2$Te$_3$. By combining the perturbation theory and the WKB approximation we calculate the LLs in the presence of hexagonal warping. We predict that due to the degeneracy removal the evolution of LLs in the magnetic field is drastically modified.