Two dimensional gap solitons in self-defocusing media with PT-symmetric superlattice

•Gap solitons are studied in self-defocusing media with PT-symmetric superlattice.•Fundamental solitons, multi-peaked solitons and vortex solitons can exist in nonlinear media with PT-symmetric potential.•The stability properties are studied by linear stability analysis and direct numerical simulation.

A theory is presented to study the existence and stability properties of fundamental solitons, multi-peaked gap solitons and vortex solitons in self-defocusing media with PT-symmetric superlattice. In the first gap of the superlattice potential, fundamental, dipole, and in-phase quadruple solitons can exist stably within a wide parameter region, while in-phase two-peaked solitons, out-of-phase quadruple solitons and vortex solitons are always unstable. Compared with simple-lattice solitons in similar potentials, the gap solitons in superlattice have a wider stable range than those in simple-lattice.