Nonsingular vortices-skyrmions for odd Landau level fillings in 2d system

Abstract

Using gradient expansion method the particle density, the energy and the action were calculated at the formation of a vortex-skyrmion at high magnetic field. No approximation of single Landau level was used contrary to other papers on the subject. Taking into account the nearest Landau levels essentially changes the expression for the vortex energy and gives some simple physical interpretation of the main results. The local electron density coincides with the local density of states. It is shown that the formation of a vortex skyrmion gives the gain in the thermodynamic energy in the limit of alarge magnetic field and a small value of the g-factor. That means a spontaneous formation of vortices in this case. The Hopf term in the vortex-skyrmion action is calculated and corresponds to the fermionic picture.