Vortex in Maxwell-Chern-Simons models coupled to external backgrounds

We consider Maxwell-Chern-Simons models involving different nonminimal coupling terms to a non relativistic massive scalar and further coupled to an external uniform background charge. We study how these models can be constrained to support static radially symmetric vortex configurations saturating the lower bound for the energy. Models involving Zeeman-type coupling support such vortices provided the potential has a 'symmetry breaking' form and a relation between parameters holds. In models where minimal coupling is supplemented by magnetic and electric field dependent coupling terms, non trivial vortex configurations minimizing the energy occur only when a nonlinear potential is introduced. The corresponding vortices are studied numerically.