Half vortices in exciton polariton condensates

It is shown that vortices in linearly polarized polariton condensates in planar semiconductor microcavities carry two winding numbers (k, m). These numbers can be either integer or half-integer simultaneously. Four half-integer vortices (1/2, 1/2), (-1/2, -1/2), (1/2, -1/2), and (-1/2, 1/2) are anisotropic, possess the smallest energy, and define the Kosterlitz-Thouless transition temperature. The condensate concentration remains finite within the core of the half vortex and the condensate polarization becomes fully circular in the core center.