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

We present a numerical study of exciton-polariton (polariton) condensation in a staggered polariton graphene showing a gapped s-band at the \(K\) and \(K'\) valleys. The condensation occurs at \(K\) or \(K'\), at the kinetically-favorable negative mass extrema of the valence band. Considering attractive polariton-polariton interaction allows to generate a spatially extended condensate. Spontaneous symmetry breaking occurring during the condensate build-up leads to the formation of valley-polarized domains following the Kibble-Zurek scenario. The selection of a single valley breaks time-reversal symmetry and the walls separating domains exhibit a topologically-protected chiral current. This current therefore emerges as a result of the interplay between the non-trivial valley topology and the condensation-induced symmetry breaking.