Non-Hermitian topological exciton-polariton corner modes

We theoretically study two-dimensional exciton-polariton lattices and predict that non-Hermitian topological corner modes can be formed under non-resonant pumping. As a generalization of the non-Hermitian skin effect, all eigenstates are localized at the two corners in our model. This is also a higher dimensional topology compared to other proposals in exciton-polariton systems and we find that it allows propagating signals in the bulk of the system to travel around defects, which is not possible in one-dimensional topological lattices or two-dimensional lattices with Hermitian edge states. Furthermore, as all polariton states are localized away from an excitation spot, the system offers an opportunity for more accurate measurement of the polariton-polariton interaction strength as the pump-induced exciton-reservoir is spatially separated from all polariton states