Inequalities for Delta (T)/kBTc: A test for weak-coupling theory applied to high-Tc superconductors.

Abstract

High-T/sub c/ superconductors should be strong or weak-coupling superconductors depending on the mechanism responsible for superconductivity. The answer will allow one to discriminate between various theories. In order to have a definite criterion independent of band-structure effects, we investigate the effect of a rapidly varying density of states in weak-coupling Bardeen-Cooper-Schrieffer (BCS) theory. We show that, whatever the density of states, ..delta..(0)/k/sub B/T/sub c/less than or equal to2. At finite temperature, this is generalized into ..delta..(T)less than or equal to1.13..delta../sub BCS/(T) where ..delta../sub BCS/ is the standard result for a constant density of states. If the gap is anisotropic, the same inequalities must be satisfied by the minimum of the gap over the Fermi surface. These exact results allow one to test whether high-T/sub c/ superconductors are weak or strong coupling.