Gapped energy spectra around the Dirac node at the surface of a 3D topological insulator in the presence of the time-reversal symmetry

TL;DR

This paper investigates how impurity scattering and electron-gauge field interactions open a gap at the Dirac node on the surface of a 3D topological insulator, aligning with recent experimental observations.

Contribution

It demonstrates that impurity scatterings coupled with gauge fields can induce a gap at the Dirac point, providing a theoretical explanation consistent with experiments and bulk-boundary correspondence.

Findings

Impurity scattering with gauge coupling opens a gap at the Dirac node.

Results align with recent experimental findings.

Applicable to two-dimensional massless fermions.

Abstract

We discuss the excitation spectra around the Dirac node on a surface of a three-dimensional topological insulator. By using the diagrammatic expansion, we show that the coupling of an electron with the gauge field in the presence of impurity scatterings opens a gap around the Dirac node. The results are consistent with a recent experimental finding by T. Sato,et. al.[ Nature Phys. \textbf{7}, 840 (2011)]. We also discuss the consistency between the present results and the bulk-boundary correspondence of the topological insulator in the presence of time reversal symmetry. The conclusion can be applied any two dimensional massless fermions.