  Photonic crystals have provided a controllable platform to examine excitingly
new topological states in open systems. In this work, we reveal photonic
topological corner states in a photonic graphene with mirror-symmetrically
patterned gain and loss. Such a nontrivial Wannier-type higher-order
topological phase is achieved through solely tuning on-site gain/loss
strengths, which leads to annihilation of the two valley Dirac cones at a
time-reversal-symmetric point, as the gain and loss change the effective
tunneling between adjacent sites. We find that the symmetry-protected photonic
corner modes exhibit purely imaginary energies and the role of the Wannier
center as the topological invariant is illustrated. For experimental
considerations, we also examine the topological interface states near a domain
wall. Our work introduces an interesting platform for non-Hermiticity-induced
photonic higher-order topological insulators, which, with current experimental
technologies, can be readily accessed.
