Avoiding umklapp dilemma in BCS superconductor theory

Abstract

According to BCS both electrical resistivity and superconductivity arise from the same electronphonon interactions. The strength of the interactions is measured by the matrix element, which in the past has always been inconsistent in the normal and superconducting states from first principles calculations. Here the difficulty is attributed to a dilemma that, in the presence of umklapp scattering, the occupancy probabilities of electron pairs in BCS theory can be doubly and contradictorily defined, together with double fermion occupations. A survival rate is introduced to avoid the umklapp dilemma from taking place in principle, that solves the historical difficulty of finding consistent resistivity and superconductivity.

On the use of Monkhorst–Pack scheme to evaluate superconductivity and the issue of umklapp electron–phonon interactions

“…We devise an alternative scheme to pair superconducting electrons to avoid conflict. 43,44 We show it can solve the historical difficulty with high accuracy in Pb and Pd.…”

“…The topic was discussed before. 43,44 We revisit it here, with additional explanations, for the convenience of the reader. In Fig.…”

Reply to Comment on ‘Reply to comment on High-T c superconductivity in H3S : pressure effects on the superconducting critical temperature and Cooper-pair distribution function’

“…This is not trivial topic. Zheng X H and Walmsley D G have quite interesting advances in that way [9,10]. In sum, the effect of the umklapp-processes in the superconductivity of high critical temperature is an open question that deserves a in-depth and detailed analysis.…”

Comment on ‘High- Tc superconductivity in H3S: pressure effects on the superconducting critical temperature and Cooper pair distribution function’

“…If the MP scheme in the QUANTUM-ESPRESSO package still is in its original form, then the umklapp phonons must all have been excluded from [1]. It has been known for some time the theoretical superconductivity always turns out to be overly strong when both normal and umklapp phonons are included in the first principles evaluations [9]. There is a recent argument calling for exclusions of some of the phonons, with theoretical justifications [5,9].…”

“…It has been known for some time the theoretical superconductivity always turns out to be overly strong when both normal and umklapp phonons are included in the first principles evaluations [9]. There is a recent argument calling for exclusions of some of the phonons, with theoretical justifications [5,9]. Perhaps the practice to use the MP scheme to evaluate superconductivity could somehow be linked to that recent argument.…”