Nonrelativistic Chern-Simons vortex solitons in external magnetic field

Abstract

We study 2+1-dimensional Chern-Simons gauge theories with external magnetic field $B$ and the self-interaction ${|\ensuremath{\psi}|}^{4}$ 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 ${g}_{c}>g>\ensuremath{-}{g}_{c}$, with $\ifmmode\pm\else\textpm\fi{}{g}_{c}$ the critical coupling constants. When ${g}_{c}>g>0$ the system has an excitation with gap; when $0>g>\ensuremath{-}{g}_{c}$ its spectrum develops the absolute minimum at a nonzero momentum. The corresponding excitation becomes gapless at $g=\ensuremath{-}{g}_{c}$, and the system is unstable for $g<\ensuremath{-}{g}_{c}$. 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 $g=\ifmmode\pm\else\textpm\fi{}{g}_{c}$. 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.