Thermal fluctuations, quenched disorder, phase transitions, and transport in type-II superconductors

Abstract

The effects of thermal fluctuations, quenched disorder, and anisotropy on the phases and phase transitions in type-II superconductors are examined, focusing on linear and nonlinear transport properties. In zero magnetic field there are two crossovers upon approaching ${\mathit{T}}_{\mathit{c}}$, first the ‘‘Ginzburg’’ crossover from mean-field behavior to the universality class of an uncharged superfluid, and then, much closer to ${\mathit{T}}_{\mathit{c}}$ for strongly type-II systems, a crossover to the universality class of a charged superfluid. The primary focus of this paper is on the behavior in the presence of a penetrating magnetic field. In a clean system the vortex-lattice phase can melt due to thermal fluctuations; we estimate the phase boundary in a variety of regimes. Pinning of vortices due to impurities or other defects destroys the long-range correlations of the vortex lattice, probably replacing it with a new vortex-glass phase that has spin-glasslike off-diagonal long-range order and is truly superconducting, in contrast to conventional theories of ‘‘flux creep.’’ The properties of this vortex-glass phase are examined, as well as the critical behavior near the transition from the vortex-glass to the vortex-fluid phase. The crossover from lattice to vortex-glass behavior for weak pinning is also examined. Linear and nonlinear conductivity measurements and other experiments on the high-${\mathit{T}}_{\mathit{c}}$ superconductors Y-Ba-Cu-O and Bi-Sr-Ca-Cu-O are discussed in light of the results. The latter is found to exhibit strongly two-dimensional behavior over large portions of its phase diagram.