Layered superconductors. I. Vortex and fluxon phase transitions

A system of superconducting layers with spacing d, in-layer penetration depth λe 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 Tv. When λed a finite-size transition at Tveff>Tv distinguishes this system from an XY model. When J0, but vortices are neglected, Josephson fluxon loops lead to a distinct phase transition at Tf>Tv in which a significant second nearest-layer coupling is generated. Competing vortices and fluxon loops lead to a three-dimensional phase transition at Tc, where Tv<Tc<Tf. For CuO2-based superconductors (λed) Tc is near Tf if TcJTcexp(-Ec′/Tc), where Ec′ is a renormalized vortex-core energy; Tc drops to Tv as J is decreased, accounting for data on YBa2Cu3O7/PrBa2Cu3O7 superlattices.