Pairing of electrons in superconductors

Crystals may contain electronic real-space-eigenstates as ground states, which are spatially much larger than one unit cell, such as impurity states, standing waves at Brillouin zone edges, states of Anderson localization, etc. Every eigenstate is usually occupied by two conduction electrons with opposite spins, forming a singlet pair. Notably: if the eigenstate is limited in real space, then the excitation energy of each singlet electron is not necessarily negligible, so below a certain temperature the singlet pair can be lasting. Isn't this a long-debated pairing mechanism in superconductors ?

Put some equations into your inital post then it would be easier to comprehend. At least for me.

The math to the question is available in a paper
https://arxiv.org/abs/1501.04978

Sadly, we don't discuss personal research at PF even if its available as an arxiv paper. Once the paper gets published in a reputable journal then we can reconsider our position.

Closing this thread.

Jedi