Umklapp scattering of pairs in BCS superconductivity theory

Abstract

The BCS theory of superconductivity is extended to recognize pairing of electrons by both normal and umklapp phonon scattering. Application of the variational approach shows that coexistence of normal and umklapp scattering frustrates superconductivity.

Empirical rule to reconcile Bardeen–Cooper–Schrieffer theory with electron–phonon interaction in normal state

“…with the N and U-processes being illustrated by the solid and dashed curved arrows in figure 1, respectively, both arrows start from k. Also consider the event arising from the second term in the brackets: which is not normalized unless h N or h U vanishes, consistent with the conclusion in [30][31][32].…”

“…This is a manifestation of the algebraic contradiction within the original BCS theory [30][31][32] that the ground state electronic wavefunction cannot be normalized when normal and umklapp scattering coexist, see appendix.…”

Discrepancy between theory and measurement of superconducting vanadium

“…It is designed to overcome: (1) conceptual and numerical difficulties of the BCS theory and (2) uncertainty associated with l à . It is justified by its highly accurate first principles calculations for superconducting niobium, lead, [41][42][43][44][45][46][47][48] Contents lists available at ScienceDirect Physica C j o u r n a l h o m e p a g e : w w w .…”

“…Which scenario should we follow? That is the dilemma [1]. This dilemma has an alternative manifestation.…”

“…Some time ago we identified a fundamental conceptual difficulty in the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity [1,2]. Independently, in a thorough review of the theory, Hirsch concluded that it ''is fundamentally flawed'' and ''may be destined to be overhauled just as other established scientific theories of the past have been overhauled'' [3].…”