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 (psi)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 > g(c), and the symmetry-breaking phase for g(c) > g > -g(c), with +/- g(c) the critical coupling constants. When g(c) > g > 0 the system has an excitation with gap; when 0 > g > -g(c) its spectrum develops the absolute minimum at a nonzero momentum. The corresponding excitation becomes gapless at g = -g(c), and the system is unstable for g < -g(c). 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 = +/- g(c). 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.