Vortex gap solitons in spin–orbit-coupled Bose–Einstein condensates with competing nonlinearities

The formation and dynamics of full vortex gap solitons (FVGSs) are investigated in two-component Bose–Einstein condensates with spin–orbit coupling (SOC), Zeeman splitting (ZS), and competing cubic and quintic nonlinear terms, while the usual kinetic energy is neglected, assuming that it is much smaller than the SOC and ZS terms. Unlike previous SOC system with the cubic-only attractive nonlinearity, in which solely semi-vortices may be stable, with the vorticity carried by a single component, the present system supports stable FVGS states, with the vorticity present in both components (such states are called here “full vortex solitons”, to stress the difference from the half-vortices). They populate the bandgap in the system’s linear spectrum. In the case of the cubic self-attraction and quintic repulsion, stable FVGSs with a positive effective mass exist near the top of the bandgap. On the contrary, the system with cubic self-repulsion and quintic attraction produces stable FVGSs with a negative mass near the bottom of the bandgap. Mobility and collisions of FVGSs with different topological charges are investigated too. •We reveal that full vortex gap solitons (FVGSs) exist at the spectral bandgap of two-component BECs.•We found that FVGSs with positive/negative effective mass exist at the top/bottom of the bandgap.•The stability and collision dynamics of FVGSs with different topological charges were studied.