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After studying the BCS theory of superconductivity, I do not understand this quote from my notes:

"The phase of the BCS wavefunction is well defined."

I do not see this "phase" from the coherent state form of the BCS ground state. What is it?

Qmechanic
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Vinicius Ferreira
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  • You might find this article by Anderson helpful: http://journals.aps.org/rmp/abstract/10.1103/RevModPhys.38.298 – Tuhin Subhra Mukherjee Sep 01 '16 at 00:46
  • Simply put, the phase is the $\phi$ in the expression for the wavefunction given here: https://physics.stackexchange.com/questions/339747/what-is-the-link-between-the-bcs-ground-state-and-superconductivity?rq=1 – Rococo Sep 05 '17 at 04:22
  • This question is related to these ones : https://physics.stackexchange.com/q/284314/16689 and https://physics.stackexchange.com/q/310519/16689 – FraSchelle Nov 02 '17 at 09:23

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It just means that in the BCS ground state, all the electrons form bosonic pair states that condense in a single wavefunction, which hase a phase $\Phi_0$. In this case you can say that all the electrons "share" the same phase $\Phi_0$.

This is not the case in a general metallic state where electrons are much less correlated : their relative phases are random. In this case you say that the "global phase" is not well-defined.

Dimitri
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