CRITICAL-TEMPERATURE OF SUPERCONDUCTORS - EXACT SOLUTION FROM ELIASHBERG EQUATIONS ON THE WEAK-COUPLING SIDE

We solve exactly the Eliashberg equations for the critical temperature of a superconductor in the weak-coupling limit, * 0 for a general Eliashberg function 2F(). We show that in this regime the best choice for the characteristic frequency is log in the sense that the dependence of Tc on the shape of 2F() is optimally included in this way. However, there is an additional dependence of Tc on the shape of 2F(), which is studied in detail. This leads to a uniform decrease of Tc as the spectral width increases, for fixed log. We show that, in this weak-coupling regime, the critical temperature depends only on the large-scale structure of the spectrum. © 1990 The American Physical Society.