Supercurrent flow with large superconductor gap in cuprates: resurrection of phonon-mediated Cooper pairs

Abstract

We systematically explore the correctness of the Bardeen–Cooper–Schrieffer (BCS) Hamiltonian where the BCS-type electron–phonon interaction is unambiguously reinforced as the only viable attractive interaction between two electrons in cuprate superconductors because phonon-induced scattering is effectively nil for Cooper pairs (in its original form), and also phonons are not required to Bose condense. Here, we prove that (i) the Cooper-pair binding energy can be strengthened to obtain high superconductor transition temperature () and (ii) the existence of a generalized electron–phonon potential operator that can induce the finite-temperature phase transition between superconducting and strange metallic phases. To lend support for this extended BCS Hamiltonian, we derive the Fermi–Dirac statistics for Cooper-pair electrons, which correctly captures the physics of strongly bounded Cooper-pair break up with respect to changing temperature or superconductor gap (). Finally, we further extend the BCS Hamiltonian within the ionization-energy theory formalism to prove (iii) the existence of optimal doping that has maximum or , and (iv) that the specific heat capacity jump at in cuprates is due to finite-temperature phase transition. Along the way, we expose the precise microscopic reason why predicting (not guessing) a superconductor properly is a hard problem within any theory that require pairing mechanism.