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

We study the zero-temperature phase diagram and fractional excitations when a thin film of 3D topological insulator has two competing masses: T-symmetric exciton condensation and the 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 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.