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 $\nu =1/q$, 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.

4 pages. to be published in J. Phys. Soc. Jpn. Vol.67 No.10. Three references are added

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