  The spontaneous formation of lattice structure of quantized vortices is a
characteristic feature of superfluidity in closed systems under thermal
equilibrium. In exciton-polariton Bose-Einstein condensate, which is a typical
example of macroscopic quantum state in open systems, spontaneous vortex
lattices have also been proposed by not yet observed. Here, we take into
account the finite decay rate of exciton reservoir, and theoretically
investigate the vortex structures in circularly pumped polariton Bose-Einstein
condensate. Our results show that a decreasing reservoir decay rate can reduce
the number of vortices and destabilize the lattice structure, hence is
unfavorable to the formation and observation of vortex lattices. These
detrimental effects can be prevailed by applying an external angular momentum.
