We study the zero-temperature phase diagram and fractional excitation when athin film of 3D topological insulator has two competing masses: T- symmetricexciton condensation and T- breaking Zeeman effect. Two topologically distinctphases are identified: in one, the quasiparticles can be viewed as in a quantumspin Hall phase, and in the other a quantum anomalous Hall phase. The vorticesof the exciton order parameter can carry fractional charge and statistics ofelectrons in both phases. When the system undergoes the quantum phasetransition between these two phases, the charges, statistics and the number offermionic zero mode of the excitonic vortices are also changed. We derive theeffective field theory for vortices and external gauge field by directlyintegrating out fermions and present an explicit wave function for thefermionic zero mode localized at the excitonic vortices with or without orbitalmagnetic field. The quantum phase transition can be measured by optical Faradayor Kerr effect experiments, and in closing we discuss the conditions requiredto create the excitonic condensate.
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