A classification of the ground states and topological defects in a rotating two-component Bose-Einstein condensate

We classify the ground states and topological defects of a rotating two-component condensate when varying several parameters: the intracomponent coupling strengths, the intercomponent coupling strength and the particle numbers.No restriction is placed on the masses or trapping frequencies of the individual components. We present numerical phase diagrams which show the boundaries between the regions of coexistence, spatial separation and symmetry breaking. Defects such as triangular coreless vortex lattices, square coreless vortex lattices and giant skyrmions are classified. Various aspects of the phase diagrams are analytically justified thanks to a non-linear $\sigma$ model that describes the condensate in terms of the total density and a pseudo-spin representation.