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

Xue-Heng Zheng, D George Walmsley

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)224520
Number of pages8
JournalPhysical Review B
Volume76
DOIs
Publication statusPublished - 2007

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