Dynamical gap generation in topological insulators

Abstract

We developed a quantum field theoretical description for the surface states of three-dimensional topological insulators. Within the relativistic quantum field theory formulation, we investigated the dynamics of low-lying surface states in an applied transverse magnetic field. We argued that, by taking into account quantum fluctuations, in three-dimensional topological insulators there is dynamical generation of a gap by a rearrangement of the Dirac sea. By comparing with available experimental data we found that our theoretical results allowed a consistent and coherent description of the Landau level spectrum of the surface low-lying excitations. Finally, we showed that the recently detected zero-Hall plateau at the charge neutral point could be accounted for by chiral edge states residing at the magnetic domain boundaries between the top and bottom surfaces of the three-dimensional topological insulator.