Nonrelativistic Chern-Simons vortex solitons in external magnetic field

We study (2+1)-dimensional Chern-Simons gauge theories with external magnetic field B and the self-interaction |ψ|4 of the matter field. It is shown that the system has three phases depending on the strength g of the self-interaction. They are the symmetry-preserving phase for g>gc, and the symmetry-breaking phase for gc>g>-gc, with ±gc the critical coupling constants. When gc>g>0 the system has an excitation with gap; when 0>g>-gc its spectrum develops the absolute minimum at a nonzero momentum. The corresponding excitation becomes gapless at g=-gc, and the system is unstable for g<-gc. We then analyze vortex solitons which are anyons. Nontopological (topological) vortices are relevant in the symmetry-preserving (-breaking) phase. The charge, spin, and mass of these vortices are calculated. These vortices can be analyzed analytically at the critical points g=±gc. The static energy of self-dual topological vortices is obtained explicitly, and is expressed as a spin-magnetic interaction. We also present analytic time-dependent solutions of nontopological vortices, which describe vortex solitons moving along the cyclotron orbit in the external magnetic field