A Treatise on the Magnetic Vector Potential by Kristján Óttar Klausen

Author:Kristján Óttar Klausen
Language: eng
Format: epub
ISBN: 9783030522223
Publisher: Springer International Publishing

(5.20)

If the magnetic vector potential is constant in a volume of radius we obtain the London equation (5.9) from (5.19).

There is an argument for the coherence length based on the uncertainty principle: The superconducting phenomena comes into play at the critical temperature and the electrons have momentum of the order where is the Boltzmann constant and is the Fermi velocity. Then according to the uncertainty principle

(5.21)

with a being a material constant [3].

As a final note on the conceptual meaning of the coherence length, it can be shown that the wavefunction of a single Cooper pair, which will be discussed in Sect. 5.9, has a spatial extent of the same order of magnitude as [6]. The theories of London and Pippard contain neither wavefunctions nor Cooper pairs and are both based purely on electromagnetism and phenomenology.

Temperature dependent Ginzburg-Landau coherence length

Before a microscopic theory of superconductivity was formulated, Ginzburg and Landau put forth a theory based mostly on intuition [6]. The need for a more general model than that of the London equations was evident due to their prediction of a negative surface energy at the interface between the superconducting and normal state, in contradiction to the observed positive surface energy [8]. They introduced an effective wavefunction describing superconducting electrons locally with

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