Quantum phase transition and fractional excitations in a topological insulator thin film with Zeeman and excitonic masses

TL;DR

This paper investigates the phase diagram and fractional excitations in a topological insulator thin film with competing Zeeman and excitonic masses, revealing topologically distinct phases and fractionalized vortices.

Contribution

It introduces a detailed analysis of the quantum phase transition between quantum spin Hall and quantum anomalous Hall phases with fractional excitations in topological insulator thin films.

Findings

Identification of two topologically distinct phases.

Fractional charge and statistics of vortices in both phases.

Change in fermionic zero modes during the phase transition.

Abstract

We study the zero-temperature phase diagram and fractional excitation when a thin film of 3D topological insulator has two competing masses: T- symmetric exciton condensation and T- breaking Zeeman effect. Two topologically distinct phases are identified: in one, the quasiparticles can be viewed as in a quantum spin Hall phase, and in the other a quantum anomalous Hall phase. The vortices of the exciton order parameter can carry fractional charge and statistics of electrons in both phases. When the system undergoes the quantum phase transition between these two phases, the charges, statistics and the number of fermionic zero mode of the excitonic vortices are also changed. We derive the effective field theory for vortices and external gauge field by directly integrating out fermions and present an explicit wave function for the fermionic zero mode localized at the excitonic vortices with or without orbital magnetic field. The quantum phase transition can be measured by optical Faraday or Kerr effect experiments, and in closing we discuss the conditions required to create the excitonic condensate.