Vortex and fluxon phase transitions in layered superconductors

The system of superconducting layers with Josephson coupling J is studied. The ordering temperature ${\mathit{T}}_{\mathit{f}}$ for the fluxon loops parallel to the layers is shown to determine the transition temperature ${\mathit{T}}_{\mathit{c}}$ of the system, except when J is exponentially small; in the latter case ${\mathit{T}}_{\mathit{c}}$ drops towards the J=0 vortex transition, accounting for data on ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$/${\mathrm{PrBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ superlattices. A magnetic field parallel to the layers produces a sequence of phases in which the induced fluxon lines are l layers apart. For l>8 nd J not too small, phases with two-dimensional fluxon correlations occur near ${\mathit{T}}_{\mathit{c}}$; this accounts for the observed V∼${\mathit{l}}^{\mathit{a}\left(\mathit{T}\right)}$ current-voltage relation in high-${\mathit{T}}_{\mathit{c}}$ superconductors.