2008/06/21 by Fortes, M., de Llano, M., Solis, M. A.
#FOS: Physical sciences #Superconductivity (cond-mat.supr-con)
paper · doi:10.48550/arxiv.0806.3492
When both two-electron and two-hole Cooper-pairing are treated on an equal footing in the ladder approximation to the Bethe-Salpeter (BS) equation, the zero-total-momentum Cooper-pair energy is found to have two real solutions E0BS=± 2ℏ ω_D%/√e2/λ+1 which coincide with the zero-temperature BCS energy gap Δ=ℏ ωD/\sinh (1/λ) in the weak coupling limit. Here, ℏ ωD is the Debye energy and λ≥ 0 the BCS model interaction coupling parameter. The interpretation of the BCS energy gap as the binding energy of a Cooper-pair is often claimed in the literature but, to our knowledge, never substantiated even in weak-coupling as we find here. In addition, we confirm the two purely-imaginary solutions assumed since at least the late 1950s as the only solutions, namely, E0BS=± i2ℏ ωD/√e2/λ-1.