Cancellation of quantum anomalies and bosonization of three-dimensional time-reversal symmetric topological insulators

TL;DR

This paper investigates the surface states of three-dimensional time-reversal symmetric topological insulators using bosonization, revealing how quantum anomalies underpin the existence of gapless surface states and proposing a bosonic representation of these fermions.

Contribution

It introduces a bosonic theory capturing the surface states of 3D topological insulators, highlighting the role of quantum anomalies in their existence and extending the theory to include surface electron dynamics.

Findings

Quantum anomalies explain the presence of gapless surface states.

Bosonic theory with topological terms models surface Dirac fermions.

Surface fermions can be represented within a bosonic framework.

Abstract

The strong time-reversal symmetric (TRS) topological insulator (TI) in three space dimensions features gapless surface states in the form of massless Dirac fermions. We study these surface states with the method of bosonization, and find that the resulting bosonic theory has a topological contribution due to the parity anomaly of the surface Dirac fermions. We argue that the presence of a quantum anomaly is, in fact, the main reason for the existence of a surface state, by the principle that anomalies of a surface and bulk must cancel. Inspecting other classes of topological insulators, we argue that this principle holds in general. Moving beyond purely topological considerations, we incorporate the dynamics of the surface electron states into the bosonic theory. Additionally, we discuss the thermodynamics of the bosonic theory and propose a representation of the surface Dirac fermions in terms of the bosonic fields.