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Can superconducting electron pairs be annihilated when the pairs flow in an eternal supercurrent?

Posted: Sun Nov 13, 2022 2:27 am
by StanislavDolgopolov
A simple question in conventional theories of superconductivity seems to be open. Imagine, in a mercury ring (superconductivity below Tc=4.15 K) we establish a persistent supercurrent at 2 K. After that we increase temperature, say from 2 K to 3 K. At 3 K the established supercurrent is running. According to the BCS theory of superconductivity, the pair density smoothly decreases at warming, i.e. a not negligible fraction of pairs annihilates. Electrons of annihilated pairs become normal and lose their ordered supercurrent momentum on the atom lattice, so the BCS-supercurrent must smoothly decrease at warming. However, in all experiments the running supercurrent remains constant at warming and abruptly disappears at critical temperature; thus the pair annihilation (assumed in BCS) doesn’t take place.
Do the pairs really annihilate in the eternal supercurrent?
So far this paradox is open.