  We study the formation of topological defects (quantum vortices) during the
formation of a 2D polariton condensate at the $\Gamma$ 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 $0.95\pm0.05$.
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.
