Coulomb repulsion and Tc in BCS theory of superconductivity

X. H. Zheng; D. G. Walmsley

doi:10.1103/PhysRevB.71.134512

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Coulomb repulsion and Tc in BCS theory of superconductivity

X. H. Zheng, D. G. Walmsley

DOI 10.1103/PhysRevB.71.134512 · Physical Review B

T1

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Abstract

Coulomb repulsion among the many electrons in a metal is in a balance, which can be toppled by even a weak electron-phonon attractive interaction. Therefore neglecting the Coulomb term from the BCS reduced Hamiltonian has little effect on Tc. This is shown by a field-theoretic argument, an analysis based on the Bogoliubov model potential and a direct numerical calculation. Detailed knowledge about electrons and phonons for various materials can be incorporated into the BCS theory through a refined treatment of the self-consistent gap equation. Consequently the universal ratio 3.5 in the BCS theory is replaced by a range of values varying from 3.51 for Ga to 4.76 for Hg. It is found that the phonon cutoff frequency is much lower than the Debye frequency. Extraordinarily high Tc could be expected if all phonons were involved in pairing electrons in a BCS superconductor.

Source-reported materials — not catalogue approval

Formula	Reported Tc (K)	Pressure (GPa)	Type
Zn Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	—	Pressure not reported	unknown
Cd Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	—	Pressure not reported	unknown
Hg Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	—	Pressure not reported	unknown
Al Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	—	Pressure not reported	unknown
Ga Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	—	Pressure not reported	unknown
In Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	—	Pressure not reported	unknown
Tl Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	—	Pressure not reported	unknown
Sn Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	—	Pressure not reported	unknown
Pb Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	—	Pressure not reported	unknown
Nb Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	—	Pressure not reported	unknown
Ta Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	—	Pressure not reported	unknown