  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.
