Layered superconductors. I. Vortex and fluxon phase transitions

A system of superconducting layers with spacing d, in-layer penetration depth ${\lambda }_{\mathrm{e}}$ and Josephson coupling between neighboring layers J is studied. When J=0 the system exhibits a two-dimensional (2D) phase transition of vortex unbinding at a temperature ${\mathrm{T}}_{\mathrm{v}}$. When ${\lambda }_{\mathrm{e}}$≲d a finite-size transition at ${\mathrm{T}}_{\mathrm{v}}^{\mathrm{eff}}$>${\mathrm{T}}_{\mathrm{v}}$ distinguishes this system from an XY model. When J≠0, but vortices are neglected, Josephson fluxon loops lead to a distinct phase transition at ${\mathrm{T}}_{\mathrm{f}}$>${\mathrm{T}}_{\mathrm{v}}$ in which a significant second nearest-layer coupling is generated. Competing vortices and fluxon loops lead to a three-dimensional phase transition at ${\mathrm{T}}_{\mathrm{c}}$, where ${\mathrm{T}}_{\mathrm{v}}$<${\mathrm{T}}_{\mathrm{c}}$<${\mathrm{T}}_{\mathrm{f}}$. For ${\mathrm{CuO}}_2$-based superconductors (${\lambda }_{\mathrm{e}}$≫d) ${\mathrm{T}}_{\mathrm{c}}$ is near ${\mathrm{T}}_{\mathrm{f}}$ if ${\mathrm{T}}_{\mathrm{c}}$≳J≫${\mathrm{T}}_{\mathrm{c}}$exp(-${\mathrm{E}}_{\mathrm{c}}^{\prime }$/${\mathrm{T}}_{\mathrm{c}}$), where ${\mathrm{E}}_{\mathrm{c}}^{\prime }$ is a renormalized vortex-core energy; ${\mathrm{T}}_{\mathrm{c}}$ drops to ${\mathrm{T}}_{\mathrm{v}}$ as J is decreased, accounting for data on ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$/${\mathrm{PrBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$...