Textbook BCS theory seems to be blind to the fact that the electron energy bands may "bend" or overlap, or the fact that the Fermi surface is not spherical because of the crystalline lattice. We know that the conductivity properties of a normal metal depend on the band structure (at least the bands close to the Fermi surface). How does a crystal structure (or Bloch states) influence the superconducting state?
Question: How does the band structure impact the properties of a crystalline superconductor? I can not find any clear reference.
Edit: the comment by @rpsml got the spirit of this question and pointed out this paper that I will try to read in the next days, Bardeen-Cooper-Schrieffer Theory of Superconductivity in the Case of Overlapping Bands (1959). Another related question is What is the difference of the gap between superconductor and insulator?
