Interacting quantum fluid in a polariton topological insulator

We study Bogoliubov excitations of a spinor Bose Einstein condensate in a honeycomb periodic potential, in the presence of a Zeeman field and of a spin-orbit coupling specific for photonic systems, which is due to the energy splitting between TE and TM polarized eigenstates. We also consider spin-anisotropic interactions typical for cavity polaritons. We show that the non-trivial topology of the single particle case is also present for the interacting system. At low condensate density, the topology of the single-particle bands is transferred to the bogolon dispersion. At a critical value, the self-induced Zeeman field at the Dirac points of the dispersion becomes equal to the real Zeeman field and then exceeds it. The gap is thus closed and then re-opened with inverted Chern numbers. This change of topology is accompanied by a change of the propagation directions of the one-way edge modes. This result demonstrates that the chirality of a topological insulator can be reversed by collective effects in a Bose-Einstein condensate.