## Abstract

We derive Poisson's equation in the single-vortex state of type II superconductors in a conserved approximation in both dynamical and static cases. The charge and current vertex functions in the chain approximation are expressed in terms of the solutions of the Bogoliubov-de Germes equation. We rigorously prove that these vertex functions satisfy the Ward-Takahashi relation. The vertex-correction in the chain approximation is, thus, consistent with the single-electron states satisfying the Bogoliubov-de Gennes equation in the single-vortex state. It is also shown that the vertex correction for the charge-charge correlation function vanishes in the static limit. The static vortex charge, thus, can be calculated by solving Poisson's equation in the lowest-order approximation.

Original language | English |
---|---|

Pages (from-to) | 2102-2109 |

Number of pages | 8 |

Journal | journal of the physical society of japan |

Volume | 70 |

Issue number | 7 |

DOIs | |

Publication status | Published - 2001 Jul 1 |

## Keywords

- Bogoliubov-de Gennes equation
- Poisson' equation
- Type II superconductors
- Vortex charge

## ASJC Scopus subject areas

- Physics and Astronomy(all)