### 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 language | English |
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Article number | 5 |

Journal | European Physical Journal B |

Volume | 86 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2013 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

### Cite this

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**Spectrum of the vortex bound states of the dirac and Schrödinger Hamiltonian in the presence of superconducting gaps.** / Cheng, Chi-Ho.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Spectrum of the vortex bound states of the dirac and Schrödinger Hamiltonian in the presence of superconducting gaps

AU - Cheng, Chi-Ho

PY - 2013/1/1

Y1 - 2013/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84920670678&partnerID=8YFLogxK

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U2 - 10.1140/epjb/e2012-30529-8

DO - 10.1140/epjb/e2012-30529-8

M3 - Article

VL - 86

JO - European Physical Journal B

JF - European Physical Journal B

SN - 1434-6028

IS - 1

M1 - 5

ER -