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We present a numerical study of exciton-polariton (polariton) condensation ina staggered polariton graphene showing a gapped s-band at the $K$ and $K'$valleys. The condensation occurs at $K$ or $K'$, at the kinetically-favorablenegative mass extrema of the valence band. Considering attractivepolariton-polariton interaction allows to generate a spatially extendedcondensate. Spontaneous symmetry breaking occurring during the condensatebuild-up leads to the formation of valley-polarized domains following theKibble-Zurek scenario. The selection of a single valley breaks time-reversalsymmetry and the walls separating domains exhibit a topologically-protectedchiral current. This current therefore emerges as a result of the interplaybetween the non-trivial valley topology and the condensation-induced symmetrybreaking.

Domain-wall topology induced by spontaneous symmetry breaking in polariton graphene