Article
Quasi-classical model for real space shape of the Cooper pair probability density
E. F. Talantsev
M.N. Mikheev Institute of Metal Physics, Ural Branch, Russian Academy of Sciences, 18, S. Kovalevskoy St., Ekaterinburg, 620108, Russia
e-mail: evgeny.talantsev@imp.uran.ru
УДК 538.945
Abstract
Within Bardeen-Cooper-Schrieffer theory of superconductivity, two electrons form the Cooper pair in the momentum space. However, it is a challenging task to represent the Cooper pair probability density in real space. Here we proposed a quasi-classical three dimensional model for the Cooper pair probability density shape in a real space, which is appeared as a direct consequence to describe the Meissner-Ochsenfeld critical field, Bc,MO (which is the thermodynamic critical field in Type-I superconductors, and lower critical field in Type-II superconductors) by the equation Bc,MO= 1/2μ0nμBln(1+√2ξ/λ), where μ0 is the magnetic permeability of free space, n is the Cooper pair bulk density, μB is the Bohr magneton, and λ is the London penetration depth, and ξ is the coherence length. As a result, the Meissner-Ochsenfeld field can be defined as the field at which each Cooper pair exhibits the diamagnetic moment of one Bohr magneton with a multiplicative pre-factor of 1/2ln(1+√2λ/ξ). Based on quasi-classical interpretation of this result, in this study we proposed that the probability density of the Cooper pair in real space can be represented as a toroid with an inner radius ξ and an outer radius of ξ + √2λ. This means that the superconducting transition is associated not only with the charge carrier pairing, but that the pairs exhibit a new topological state with genus 1.
Keywords: cooper pair; topological phase transition; coherence length; London penetration depth.
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