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We investigate the properties of a two-dimensional \emph{spinor} microcavitypolariton system driven by a linearly polarised continuous pump. In particular,we establish the role of the elementary excitations, namely the so-calledhalf-vortices and full-vortices; these objects carry a quantum rotation only inone of the two, or both, spin components respectively. Our numerical analysisof the steady-state shows that it is only the half-vortices that are present inthe vortex-antivortex pairing/dissociation responsible for theBerezinskii-Kosterlitz-Thouless transition. These are the relevant elementaryexcitations close to the critical point. However, by exploring thephase-ordering dynamics following a sudden quench across the transition weprove that full-vortices become the relevant excitations away from the criticalpoint in a deep quasi-ordered state at late times. The time-scales forhalf-vortices binding into full vortices are much faster than thevortex-antivortex annihilations.

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