Two-dimensional multipeak gap solitons supported by parity-time-symmetric periodic potentials.

We report on the existence and stability of the two-dimensional multipeak gap solitons in a parity-time-symmetric periodic potential with defocusing Kerr nonlinearity. We investigate the multipeak solitons with all the peaks of the real parts in-phase. It is found that these solitons can be stable in the first gap. The system can support not only the stable solitons with even number peaks, but also the stable solitons with odd number peaks. The transverse energy flow vector of these solitons is also studied.