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

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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.

Original languageEnglish
Article number5
JournalEuropean Physical Journal B
Volume86
Issue number1
DOIs
Publication statusPublished - 2013 Jan 1

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Hamiltonians
Vortex flow
vortices
Electron energy levels
Magnetic fields
Fermions
Angular momentum
Chemical potential
magnetic fields
energy
angular momentum
fermions
shift

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

Cite this

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abstract = "We investigate the vortex bound states of both Schr{\"o}dinger 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 Schr{\"o}dinger 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.",
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