Full and fractional defects across the Berezinskii-Kosterlitz-Thouless transition in a driven-dissipative spinor quantum fluid

We investigate the properties of a two-dimensional spinor microcavity polariton system driven by a linearly polarized continuous pump. In particular, we establish the role of the elementary excitations, namely, the socalled half-vortices and full vortices; these objects carry a quantum rotation only in one of the two, or both, spin components, respectively. Our numerical analysis of the steady state shows that it is only the half-vortices that are present in the vortex-antivortex pairing and dissociation responsible for the Berezinskii-Kosterlitz-Thouless transition. These are the relevant elementary excitations close to the critical point. However, by exploring the phase-ordering dynamics following a sudden quench across the transition we prove that full vortices become the relevant excitations away from the critical point in a deep quasi-ordered state at late times. The time scales for half-vortices binding into full vortices are much faster than the vortex-antivortex annihilations.