We predict three-dimensional vortex solitons in a Bose-Einstein condensate under a complex potential,which is the combination of a two-dimensional parabolic trap along the transverse radial direction and a one-dimensional optical-lattice potential along the z axis direction.The vortex solitons are built in the form of a layer-chain structure made of several fundamental vortices along the optical-lattice direction.This has not been reported before in the three-dimensional Bose-Einstein condensate.By using a combination of the energy density functional method with direct numerical simulation,we find three-dimensional vortex solitons with topological charges χ=1,χ=2,and χ=3.Moreover,the macroscopic quantum tunneling and chirp phenomena of the vortex solitons are shown in the evolution.Therein,the occurrence of macroscopic quantum tunneling provides the possibility for the experimental realization of quantum tunneling.Specifically,we successfully manipulate the vortex solitons along the optical lattice direction.The stability limits for dragging the vortex solitons from an initial fixed position to a prescribed location are further pursued.
