Eur. Phys. J. B (2013) 86: 5
https://doi.org/10.1140/epjb/e2012-30529-8

Regular Article

Spectrum of the vortex bound states of the Dirac and Schrödinger Hamiltonian in the presence of superconducting gaps

Department of Physics, National Changhua University of Education, Taiwan

^a e-mail: phcch@cc.ncue.edu.tw

Received: 28 June 2012
Received in final form: 12 October 2012
Published online: 9 January 2013

Abstract

We investigate the vortex bound states of both Schrödinger and Dirac Hamiltonian with the s-wave superconducting pairing gap by solving the mean-field Bogoliubov-de-Gennes equations. The exact vortex bound states spectrum is numerically determined by the integration method, and also accompanied by the quasi-classical analysis. It is found that the bound state energies are proportional to the vortex angular momentum when the chemical potential is large enough. By applying the external magnetic field, the vortex bound state energies of the Dirac Hamiltonian are almost unchanged; whereas the energy shift of the Schrödinger Hamiltonian is proportional to the magnetic field. These qualitative differences may serve as an indirect evidence of the existence of Majorana fermions in which the zero mode exists in the case of the Dirac Hamiltonian only.