摘要：SummaryPast decades have witnessed the emergence and increasing expansion of parity-time (PT)-symmetric systems in diverse physical fields and beyond as they manifest entirely all-real spectra, although being non-Hermitian. Nonlinear waves in low-dimensionalPT-symmetric non-Hermitian systems have recently been explored broadly; however, understanding these systems in higher dimensions remains abstruse and has yet to be revealed. We survey, theoretically and numerically, matter-wave nonlinear gap modes of Bose-Einstein condensates with repulsive interparticle interactions in three-dimensionalPToptical lattices with emphasis on multidimensional gap solitons and vortices. Utilizing direct perturbed simulations, we address the stability and instability areas of both localized modes in the underlying linear band gap spectra. Our study provides deep and consistent understandings of the formation, structural property, and dynamics of coherent localized matter waves supported byPToptical lattices in multidimensional space, thus opening a way for exploring and stabilizing three-dimensional localized gap modes in non-Hermitian systemsGraphical abstractDisplay OmittedHighlights•3D parity-time (PT)-symmetric optical lattices are used to overcome the collapse of 3D ultracold atoms.•3D matter-wave gap solitons and vortices are found in PT-symmetric optical lattices.•Rich properties and dynamics of 3D matter-wave localized modes are disclosed.•In-depth soliton physics is provided in 3D non-Hermitian periodic physical systems.Condensed matter physics; Lattice; Nonlinear wave; Theoretical physics; Quantum mechanics
