Effects of Time Reversal Symmetry Breaking in Topological Insulators

Abstract

Conventional wisdom dictates that the conducting edge state of Bi2Se3 is protected by time reversal symmetry. However, theoretical bulk calculations and a recent experiment show that the edge state persists in the presence of a perpendicular external magnetic field of up to 5T. To address this apparent contradiction, we have developed an analytical description for the wave function of the edge state in a perpendicular magnetic field. This approximation is based on the bulk solutions of the Landau levels, where we also need to identify a novel bulk-like solution in the presence of a hard wall. Our approach has been found to agree well with numerical calculations. The wave function obtained can be used to analyse the edge state in a magnetic field directly.