Electron fractionalization for two-dimensional Dirac fermions

Fermion-number fractionalization without breaking the time-reversal symmetry was recently demonstrated for a field theory in (2+1)-dimensional space and time that describes the couplings between massive Dirac fermions, a complex-valued Higgs field carrying an axial gauge charge of 2, and a U(1) axial gauge field. Charge fractionalization occurs whenever the Higgs field either supports vortices by itself or when these vortices are accompanied by half vortices in the axial gauge field. The fractional charge is computed by three different techniques. A formula for the fractional charge is given as a function of a parameter in the Dirac Hamiltonian that breaks the spectral energy-reflection symmetry. In the presence of a charge +/- 1 vortex in the Higgs field, only the fractional charge continuously varies and, thus, can take irrational values. The simultaneous presence of a half vortex in the axial gauge field and a charge +/- 1 vortex in the Higgs field rerationalizes the fractional charge to the value 1/2.