The Spectrum of Thermodynamic Fluctuations in Short Coherence Length Superconductors

Abstract

Our current understanding of phase transitions enables us to establish a universal correspondence between critical behaviour at the transition point and symmetry of the effective Hamiltonian ℌ _eff of a given system, regardless of the specific nature of the microscopic interaction responsible for the transition. The universal validity of this correspondence requires that the critical behaviour is dominated by fluctuations of the order parameter having a wavelength much larger than the range of the above interaction. This is so for systems characterised by a long correlation (or coherence) length ξ of the order parameter. An example of these systems is given by superconducting metals and alloys with low transition temperature T _c , which are well described by the conventional ℌ _eff of the BCS theory. In this paper we discuss how the above fluctuation spectrum is modified in the opposite case of short-ξ systems. This is a relevant issue, since we can derive the ℌ_eff of a system undergoing a second order phase transition from the fluctuation spectrum. This study might elucidate the still open question of generalising the conventional BCS theory to account for the unusual properties of cuprate superconductors. Fluctuation studies are suited for determining the ℌ _eff of complex systems, such as the above materials, because only the relevant interaction driving the transition exhibits a critical behaviour in the fluctuation region, while this interaction is usually hidden among other interactions at temperatures far above T _c .