Critical temperature of superconductors: Exact solution from Eliashberg equations on the weak-coupling side

Abstract

We solve exactly the Eliashberg equations for the critical temperature of a superconductor in the weak-coupling limit λ,μ*→0 for a general Eliashberg function α2F(ω). We show that in this regime the best choice for the characteristic frequency is ωlog in the sense that the dependence of Tc on the shape of α2F(ω) is optimally included in this way. However, there is an additional dependence of Tc on the shape of α2F(ω), which is studied in detail. This leads to a uniform decrease of Tc as the spectral width increases, for fixed ωlog. We show that, in this weak-coupling regime, the critical temperature depends only on the large-scale structure of the spectrum.

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