Long-range Coulomb interaction effects on the surface Dirac electron system of a three-dimensional topological insulator

TL;DR

This paper studies how long-range Coulomb interactions influence the surface Dirac electrons in three-dimensional topological insulators, revealing enhancements in Fermi velocity, g-factor, and spin susceptibility due to these interactions.

Contribution

It provides a detailed analysis of Coulomb interaction effects on surface Dirac electrons, highlighting unique spin-related phenomena not present in other Dirac systems.

Findings

Fermi velocity is enhanced by LRCI

g-factor is increased due to LRCI

Spin susceptibility is amplified by Coulomb interactions

Abstract

The surface state of a three-dimensional topological insulator forms a two-dimensional massless Dirac electron system. In Dirac electron systems, Coulomb interaction is not screened due to the small density of states at the Fermi energy and thus the long-range Coulomb interaction (LRCI) plays a crucial role. In this paper, we investigate the surface state with chemical potential $\mu=0$ in the presence of the LRCI using the Wilsonian renormalization group. We first check the Fermi velocity enhancement in the surface Dirac system, which also occurs in a usual Dirac electron system. The most remarkable feature of the surface Dirac system is that the Dirac Hamiltonian contains not pseudo spin but real spin Pauli matrices. Because of this feature, we find the g-factor enhancement, which is a unique property of the surface Dirac system. We also investigate the explicit form of the spin susceptibility and find that the spin susceptibility is enhanced in the presence of the LRCI.