Kibble-Zurek mechanism in polariton graphene

We study the formation of topological defects (quantum vortices) during the formation of a two-dimensional (2D) polariton condensate at the $\mathrm{\ensuremath{\Gamma}}$ point of a honeycomb lattice via the Kibble-Zurek mechanism. The lattice modifies the single-particle dispersion. The typical interaction energies at the quench time correspond to the linear part of the dispersion. The resulting scaling exponent for the density of topological defects is numerically found as $0.95\ifmmode\pm\else\textpm\fi{}0.05$. This value differs from the one expected for 2D massive particles (1/2), but is indeed compatible with the one expected for a linear dispersion. We moreover demonstrate that the vortices can be pinned to the lattice, which prevents their recombination and could facilitate their observation and counting in continuous wave experiments.