Asymptotic behavior of Eliashberg gap function in the complex plane and its implications for the Coulomb pseudopotential in superconductors

X. H. Zheng; D. G. Walmsley

doi:10.1103/PhysRevB.76.224520

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Asymptotic behavior of Eliashberg gap function in the complex plane and its implications for the Coulomb pseudopotential in superconductors

X. H. Zheng, D. G. Walmsley

DOI 10.1103/PhysRevB.76.224520 · Physical Review B

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Abstract

The energy gap function in the Eliashberg formalism draws a spiral in the complex plane. A simple, efficient numerical scheme is devised to extend that spiral towards the bottom of the Fermi sea for lead, mercury, tin, and a model superconductor. The spiral is confirmed to converge to a constant value with a finite negative real part. The asymptotic behavior is explored to reveal a V-shaped dependence of the Coulomb pseudopotential μ* on the electron cutoff frequency in Pb and Hg, with a strong growth tendency when the cutoff frequency is large. A reference formula due to Allen and Dynes correctly predicts the later growth trend of μ* at large cutoff frequencies but overestimates its rate. Previous values of μ* in the literature have to be viewed critically.

Source-reported materials — not catalogue approval

Formula	Reported Tc (K)	Pressure (GPa)	Type
Pb 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
Sn Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	—	Pressure not reported	unknown
MgB2 Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	—	Pressure not reported	unknown