Poisson's Equation in the Vortex State of Type II Superconductors

Tomio Koyama

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


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 languageEnglish
Pages (from-to)2102-2109
Number of pages8
Journaljournal of the physical society of japan
Issue number7
Publication statusPublished - 2001 Jul 1


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

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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