Wave Function of the Largest Skyrmion on a Sphere

Abstract

It has been clarified that charged excitation known as a skyrmion exists around the ferromagnetic ground state at the Landau level filling factor $ν=1/q$, 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 $ν=1$ and $ν=1/3$ through exact diagonalization of the Hamiltonian for finite sized spherical systems. It is clarified that the skyrmion wave functions at $ν=1$ and $ν=1/3$ are qualitatively different: they are not related by the composite fermion transformation. Long-range behavior of the skyrmion wave function around $ν=1$ is shown to be consistent with the semiclassical picture of the skyrmion.