NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2015, 6 (3), P. 353–360
Localized states near the Abrikosov vortex core in type-II superconductors within zero-range potential model
V. L. Kulinskii – Department of Theoretical Physics, Odessa National University, Dvoryanskaya 2, 65082 Odessa, Ukraine; email@example.com
D. Yu. Panchenko – Department of Theoretical Physics, Odessa National University, Dvoryanskaya 2, 65082 Odessa, Ukraine; firstname.lastname@example.org
We propose to treat the lowest bound states near the Abrikosov vortex core in type-II superconductors on the basis of the self-adjoint extension of the Hamiltonian of Aharonov-Bohm type with the localized magnetic flux. It is shown that the Hamiltonian for the excitations near the vortex core can be treated in terms of the generalized zero-range potential method when the magnetic field penetration depth δ is much greater than the coherence length ξ i.e. in the limit κ = δ/ξ ≫ 1. In addition, it is shown that in this limit it is the singular behavior of d∆/dr(r=0) and not the details of the order parameter ∆(r) profile that is important. In support of the proposed model, we reproduce the spectrum of the Caroli-de Gennes-Matricon states and provide direct comparison with the numerical calculations of Hayashi, N. et al. [Phys. Rev. Lett. 80, p. 2921 (1998)]. In contrast to the empirical formula for the energy of the ground state in Hayashi, N. we use no fitting parameter. The parameters for the boundary conditions are determined in a self-consistent manner with Caroli-de Gennes-Matricon formula.
Keywords: Abrikosov vortex; bound states; zero-range potential.
PACS 74.25.Jb, 74.25.Ha