SUPERCONDUCTING CRITICAL-TEMPERATURE IN QUASI-2-DIMENSIONAL SYSTEMS

We calculate the superconducting critical temperature for systems consisting of weakly coupled planes. We consider an attractive-U Hubbard model in a tetragonal structure. The anisotropy is characterized by the ratio between the hopping matrix elements within the planes (t) and between them (t'). We calculate the critical temperature T(c) for the onset of off-diagonal long-range order by calculating fluctuations around the mean-field solution. For independent planes (t' = 0) T(c) is zero and each plane has a Kosterlitz-Thouless transition at a temperature TKT. As the interplane coupling increases T(c) increases very rapidly and for t'/t congruent-to 0.03 we obtain T(KT). For larger values of t' the superconducting critical temperature increases almost linearly with the interplane coupling.