Theory of Strongly Fluctuating Superconductivity

Abstract

In superconductors with short coherence lengths, such as the copper oxides, the order parameter is prone to phase fluctuations. Josephson showed that phase fluctuations are coupled to the density of Cooper pairs so that they are always accompanied by space and time varying supercurrents. In this paper we show how the variation of the order parameter, its phase, and the charge density can be mapped onto a magnetic problem by a real space extension of the pseudo-spin representation of Anderson. It is shown that at long wavelengths the charge fluctuation is asymptotically decoupled from the order parameter fluctuation so that the problem is isomorphic to the XY model. In particular, at low temperatures there exist collective excitations, the so-called phase waves, which are analogous to spin waves in magnetic systems. Two experiments are proposed to test the theoretical predictions.