Phase transitions in layered superconductors.

Abstract

A system of superconducting layers with Josephson coupling J between them is studied. When the in-layer penetration depth ${\ensuremath{\lambda}}_{\mathit{e}}$ is larger than the spacing d between layers, as in ${\mathrm{CuO}}_{2}$-based superconductors, there is a single three-dimensional transition temperature ${\mathit{T}}_{\mathit{c}}$. The ratio ${\mathit{T}}_{\mathit{c}}$/\ensuremath{\tau}, where \ensuremath{\tau}=${\mathrm{\ensuremath{\varphi}}}_{0}^{2}$/4${\mathrm{\ensuremath{\pi}}}^{2}$${\ensuremath{\lambda}}_{\mathit{e}}$, is found to vary from \ensuremath{\sim}1/8 to \ensuremath{\sim}1, being near 1/8 when J/${\mathit{T}}_{\mathit{c}}$ is exponentially small. When ${\ensuremath{\lambda}}_{\mathit{e}}$\ensuremath{\lesssim}d a two-dimensional (2D) behavior is possible; in particular, bulk superconductors separated by 2D junctions exhibit a 2D transition, below the bulk transition, in which the junctions become ordered. This 2D behavior is due to the gauge coupling and is absent in an XY model where ${\ensuremath{\lambda}}_{\mathit{e}}$\ensuremath{\rightarrow}\ensuremath{\infty}.