Zero-range potential model for the study of the ground states near the vortex core in the quantum limit

TL;DR

This paper develops a zero-range potential model to analyze the ground states near vortex cores in quantum systems, using self-adjoint extension theory and comparing analytical results with numerical data.

Contribution

It introduces a zero-range potential approach for vortex core states based on self-adjoint extension, providing analytical expressions for the ground state energy.

Findings

Derived the spectrum of vortex core excitations.

Obtained an analytical expression for ground state energy.

Validated results against numerical calculations.

Abstract

We propose the treatment of the lowest bound states near the vortex core on the basis of the self-adjoint extension of the Hamiltonian with the localized magnetic flux of Aaronov-Bohm type. It is shown that in the limit {\varkappa} >> 1 the potential for the vortex core excitations can be treated in terms of the generalized zero-range potential method. The spectrum of the Caroli-de Gennes-Matricon states is obtained and the comparison with the numerical calculations of Hayashi, N. et al. [Phys. Rev. Lett. 80, p. 2921 (1998)] is performed. The analytical expression for the ground state energy depending on the boundary condition parameter b was obtained by us.