Layered superconductors. II. Melting of parallel-flux lattice

A system of superconducting layers with Josephson coupling J between neighboring layers is studied in the presence of a magnetic field parallel to the layers. A sequence of ‘‘scrl phases’’ is produced where the induced flux lines are scrl layers apart. An scrl phase is solved by an equivalent fermion problem and its melting temperature ${\mathit{T}}_{\mathit{m}}$(scrl) is found. When J is not too small, there is a range ${\mathit{scrl}}_{\min }$scrl${\mathit{scrl}}_{\max }$ for which two-dimensional phases are possible and ${\mathit{scrl}}_{\min }$=8–10. These results account for the current-voltage relation of the form V∼${\mathit{I}}^{\mathit{a}\left(\mathit{T}\right)}$ as observed in many of the high-${\mathit{T}}_{\mathit{c}}$ superconductors.