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

TL;DR

This paper investigates vortex-skyrmion formations in 2D electron systems at high magnetic fields, revealing their energetic favorability and detailed properties without single Landau level approximation.

Contribution

It introduces a method that accounts for multiple Landau levels, providing new insights into vortex-skyrmion energetics and their physical interpretation.

Findings

Vortex-skyrmions lower the thermodynamic energy at high magnetic fields.

Including neighboring Landau levels alters vortex energy expressions.

The Hopf term aligns with a fermionic description.

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.