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

TLDR

Thermal fluctuations, quenched disorder, and anisotropy govern phase transitions in type‑II superconductors, with zero‑field crossovers from mean‑field to uncharged and charged superfluid universality classes near the critical temperature. The study investigates vortex behavior in the presence of a penetrating magnetic field. In a magnetic field, thermal fluctuations can melt the vortex lattice, while disorder induces a vortex‑glass phase with spin‑glass‑like order that transitions to a vortex fluid; the crossover from lattice to glass is examined across weak pinning regimes. Experiments on Y‑Ba‑Cu‑O and Bi‑Sr‑Ca‑Cu‑O show linear and nonlinear conductivity consistent with the theory, and Bi‑Sr‑Ca‑Cu‑O exhibits pronounced two‑dimensional behavior over much of its phase diagram.

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.