Wave Function of the Largest Skyrmion on a Sphere

TL;DR

This paper derives and compares the wave functions of skyrmions at filling factors 1 and 1/3 on a sphere, revealing qualitative differences and confirming semiclassical behavior at ν=1.

Contribution

It provides analytical wave functions for skyrmions at ν=1 and 1/3, showing they are not related by composite fermion transformation and differ qualitatively.

Findings

Wave functions at ν=1 and 1/3 are qualitatively different.

Long-range behavior at ν=1 aligns with semiclassical skyrmion picture.

Exact diagonalization confirms analytical forms for finite systems.

Abstract

It has been clarified that charged excitation known as a skyrmion exists around the ferromagnetic ground state at the Landau level filling factor $\nu=1/q$, where $q$ is an odd integer. An infinite sized skyrmion is realized in the absence of the spin-Zeeman splitting or for double-layered systems. Analytical form of the wave function is identified at $\nu=1$ and $\nu=1/3$ through exact diagonalization of the Hamiltonian for finite sized spherical systems. It is clarified that the skyrmion wave functions at $\nu=1$ and $\nu=1/3$ are qualitatively different: they are not related by the composite fermion transformation. Long-range behavior of the skyrmion wave function around $\nu=1$ is shown to be consistent with the semiclassical picture of the skyrmion.