Fluctuations and disorder in high temperature superconductors

Abstract

The special material parameters of the oxide superconductors lead to a dramatic increase of the importance of thermal and quantum fluctuations. The latter can be quantified by the Ginzburg number Gi = [T c/ H 2 c(0)ϵξ 3(0)] 2/2 and the quantum resistance Q u = (e 2/ h ̵ ) [ϱN/ ϵξ(0)] , where H c(0), ξ(0), and ϱ N denote the thermodynamic critical field, the planar coherence length (both linearly extrapolated to zero), and the planar normal resistivity. ϵ 2 = m/ M < 1 is the anisotropy parameter. In the high T c 's (specifically for YBCO) we have Gi ≅ 10 −2 and Qu ≅ 1 and thus these parameters are by orders of magnitude larger than in conventional low- T c superconductors. The large fluctuations lead to the melting of the vortex lattice well below the upper critical field line. The inclusion of quenched disorder as parametrized by the critical current density ratio j c / j o drastically changes the dynamic behavior of the vortex system ( j c and j o denote the depinning and depairing current densities). We discuss the equilibrium statistical mechanics (vortex lattice melting) and the dynamic behavior (creep) of the vortex system with a particular emphasis on the role of quantum fluctuations.