Edge states of a Bi$_2$Se$_3$ nanosheet in a perpendicular magnetic field

TL;DR

This paper develops an analytical model for the edge states of Bi$_2$Se$_3$ nanosheets in magnetic fields, explaining their persistence despite broken time-reversal symmetry and aligning well with numerical results.

Contribution

It introduces an analytical wave function description for edge states in magnetic fields, reconciling experimental observations with theoretical expectations.

Findings

Edge states persist under large magnetic fields.

Analytical wave functions match numerical calculations.

Edge states are described by bulk Landau levels plus boundary states.

Abstract

Conventional wisdom dictates that the conducting edge states of two-dimensional topological insulators of the Bi$_2$Se$_3$ family are protected by time-reversal symmetry. However, theoretical bulk calculations and a recent experiment show that the edge states persist in the presence of large external magnetic fields. To address this apparent contradiction, we have developed an analytical description for the edge-state wave function of a semi-infinite sample in a perpendicular magnetic field. Our description relies on the usual bulk Landau levels, together with additional states arising due to the presence of the hard wall, which are unnormalizable in the infinite system. The analytical wave functions agree extremely well with numerical calculations and can be used to directly analyze the behavior of the edge states in a magnetic field.