Skyrmion Excitations in Quantum Hall Systems

TL;DR

This paper investigates skyrmion excitations in quantum Hall systems with spin, analyzing their size, energy, and behavior under varying Zeeman energy using finite size calculations on a spherical surface.

Contribution

It provides a detailed analysis of skyrmion excitations, including their size and energy dependence on Zeeman energy, in quantum Hall systems with spin.

Findings

Skyrmions are the lowest energy excitations at zero Zeeman energy.

Skyrmion size decreases with increasing Zeeman energy.

Energy gaps exhibit kinks corresponding to skyrmion size changes.

Abstract

Using finite size calculations on the surface of a sphere we study the topological (skyrmion) excitation in quantum Hall system with spin degree of freedom at filling factors around $\nu=1$. In the absence of Zeeman energy, we find, in systems with one quasi-particle or one quasi-hole, the lowest energy band consists of states with $L=S$, where $L$ and $S$ are the total orbital and spin angular momentum. These different spin states are almost degenerate in the thermodynamic limit and their symmetry-breaking ground state is the state with one skyrmion of infinite size. In the presence of Zeeman energy, the skyrmion size is determined by the interplay of the Zeeman energy and electron-electron interaction and the skyrmion shrinks to a spin texture of finite size. We have calculated the energy gap of the system at infinite wave vector limit as a function of the Zeeman energy and find there are kinks in the energy gap associated with the shrinking of the size of the skyrmion. breaking ground state is the state with one skyrmion of infinite size. In the presence of Zeeman energy, the skyrmion size is determined by the interplay of the Zeeman energy and electron-electron