On Pokrovskii's anisotropic gap equations in superconductivity theory

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An existence and uniqueness theorem for Pokrovskii's zero-temperature anisotropic gap equation is proved. Furthermore, it is shown that Pokrovskii's finite-temperature equation is inconsistent with the Bardeen-Cooper-Schrieffer (BCS) theory. A reformulation of the anisotropic gap equation is presented along the line of Pokrovskii and it is shown that the new equation is consistent with the BCS theory for the whole temperature range. As an application, the Markowitz-Kadanoff model for anisotropic superconductivity is considered and a rigorous proof of the half-integer-exponent isotope effect is obtained. Furthermore, a sharp estimate of the gap solution near the transition temperature is established.

Original languageEnglish (US)
Pages (from-to)2061-2073
Number of pages13
Issue number6
StatePublished - Nov 2003

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • General Physics and Astronomy
  • Applied Mathematics


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