BCS theory has to be overhauled: Reassurance from numerical survival rate

Abstract

The BCS theory has conceptual and numerical difficulties. We have previously overhauled it with a new scheme of phonon-mediated electron pairing that can be expressed analytically in terms of an empirical pairing survival rate factor, S(q) = 0 or 1/2, depending on phonon momentum, q. Now we evaluate S(q) numerically entirely from experimental data on normal state electrical resistivity and on superconducting tunnelling conductance. The empirical and numerical S(q) are reassuringly close in aluminium and lead and particularly so in two other cases, niobium and tantalum.

Visualised predictions of gap anisotropy to test new electron pairing scheme

“…Clearly Eq. (4) helps to circumvent the BCS conceptual difficulty; see [9,10] for detailed microscopic justifications. In a series of publications we established the worth of Eq.…”

“…In a series of publications we established the worth of Eq. (4) in that it allows the same pseudopotential to be used to evaluate the electron-phonon interaction for both normal state resistivity and superconductivity with high accuracy [9,10,12,13]. Indeed it becomes clear that the new pairing potential is much better in that it is close to the resistivity-derived potential and contrasts with the BCS potential.…”

“…The BCS theory has always suffered from a numerical difficulty: there is an inconsistency in outcome when the electron-phonon interaction assumed in the theory of electrical resistivity in the normal state is used in it. The literature shows that either superconductivity from the BCS theory is too strong when the calculated resistivity is reasonable or, conversely but equivalently, resistivity is too weak when superconductivity is reasonable: somehow the phonon contribution to superconductivity is excessive and needs to be curtailed [9,10].…”

“…We have also identified a conceptual difficulty in the BCS theory [9,10]. We have introduced an empirical scheme of electron pairing to overhaul the theory both conceptually and numerically [9][10][11]. It can be presented analytically as a survival rate, S(q) = 0 or 1/2, depending on whether or not scattered electron pairs fall into the black areas in FIG.…”

“…2). Extensive tests demonstrate that the numerical difficulty of the BCS theory also is remedied to high accuracy when this consideration is taken into account [9][10][11][12][13].…”