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Calculation of the transition temperature T c of superconductors
Author(s) -
Nowotny H.,
Hittmair O.
Publication year - 1979
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2220910231
Subject(s) - superconductivity , logarithm , isotropy , phonon , condensed matter physics , mathematical physics , energy (signal processing) , physics , superconducting transition temperature , mathematics , specific heat , transition temperature , mathematical analysis , quantum mechanics
Abstract An iterative solution of the Eliashberg equations for isotropic superconductors is approximated by an analytical expression and gives as a result an equation for the superconducting transition temperature T c . For small T c ( T c ≪ mean phonon energy) a formula is derived, which agrees within a few per cent with the well‐known McMillan formula, if in this formula the mean logarithmic phonon energy ω log is taken as pre‐factor, a correction which was already proposed earlier. For large T c the (λ < ω 2 ) 1/2 behaviour of Allen and Dynes is found. Numerical results are presented for 0.5 < λ < 8, where the α 2 F (ω)‐shapes are taken corresponding to Hg, Pb, In, and Nb.