Spontaneous formation of vortices and gray solitons in a spinor polariton fluid under coherent driving

It is generally accepted that quantized vortices formed in coherent bosonic fluids are ``excitations'' and as such do not arise in a one-mode condensate at zero temperature. To excite them, one needs either inhomogeneities (impurities, rotation, etc.) or essentially finite fluctuations. Here, we predict a perfectly spontaneous formation of vortices even at zero temperature, which takes place in a homogeneous cavity-polariton system under one-mode optical excitation at normal incidence. In spite of the absence of equilibrium and U(1) invariance, this system shows a counterpart of the Berezinskii-Kosterlitz-Thouless crossover between single vortices and coupled vortex-antivortex states ranging from small dipoles to rectilinear filaments with long-range ordering.