Vortex nucleation in rotating Bose-Einstein condensates with density-dependent gauge potential

We study numerically the vortex dynamics and vortex-lattice formation in a rotating density-dependent Bose-Einstein condensate (BEC), characterized by the presence of nonlinear rotation. By varying the strength of nonlinear rotation in density-dependent BECs, we calculate the critical frequency, Ω_{cr}, for vortex nucleation both in adiabatic and sudden external trap rotations. The nonlinear rotation modifies the extent of deformation experienced by the BEC due to the trap and shifts the Ω_{cr} values for vortex nucleation. The critical frequencies, and thereby the transition to vortex-lattices in an adiabatic rotation ramp, depend on conventional s-wave scattering lengths through the strength of nonlinear rotation, C, such that Ω_{cr}(C>0)