Phenomenological theory for copper oxide high-Tcsuperconductors

A phenomenological Ginzburg-Landau model for the newly discovered high-$T_c$ superconducting series ${\mathrm{Tl}}_{\mathit{m}}$ ${\mathrm{Ba}}_2$ ${\mathrm{Ca}}_{\mathit{n}\mathrm{-}1}$ ${\mathrm{Cu}}_{\mathit{n}}$ ${\mathrm{O}}_{2\mathit{n}+\mathit{m}+2\mathrm{}}$ (m=1,2) and ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{Ca}}_{\mathit{n}\mathrm{-}1}$ ${\mathrm{Cu}}_{\mathit{n}}$ ${\mathrm{O}}_{2\mathit{n}+4\mathrm{}}$ is formulated. It is assumed that the order parameters in adjacent CuO layers are coupled through a simple Josephson-effect-like tunneling. By minimizing the free energy, expressions for the transition temperatures of the n-layer superconductors are obtained. Using the published $T_c$’s of the first members of each series, the $T_c$’s of the higher members are obtained and are in good agreement with the experimental values.