Centrosymmetric multipole solitons with fractional-order diffraction in two-dimensional parity-time-symmetric optical lattices

•Nonlinear fractional Schrödinger equation•Gap solitons in parity-time -symmetric lattices•On-site and off-site eight-pole solitons•The method of linear stability analysis Multipole solitons in higher-dimensional nonlinear Schrödinger equation with fractional diffraction are of high current interest. This paper studies multipole gap solitons in parity-time (PT)-symmetric lattices with fractional diffraction. The results obtained demonstrate that both on-site and off-site eight-pole solitons with fractional-order diffraction can be stabilized in a two-dimensional (2D) PT-symmetric optical lattice with defocusing Kerr nonlinearity. These solitons are in-phase and centrosymmetric. On-site eight-pole solitons propagate in a square formation, while off-site solitons propagate in a two-by-four formation. Both on-site and off-site solitons are found to be stable within a low-power range in the first band gap. As the Lévy index decreases, the stability regions of both on-site and off-site solitons narrow. Off-site eight-pole solitons can approach the lower edge of the first Bloch band, whereas on-site eight-pole solitons cannot. Additionally, we investigate the transverse power flow vector of these multipole gap solitons, illustrating the transverse energy flow from gain to loss regions.