Enhanced Superconductivity in Bilayered Systems

We investigate superconducting correlations in bilayered systems. The planes are described by a two-dimensional $t_{\parallel} - J_{\parallel} - U$ with $t_{\perp}$ and $J_{\perp}$ denoting the interplanar parameters. These interplanar couplings when coupled with hopping anisotropies in the planes may account for a host of unusual superconducting properties. Our main focus is to calculate superconducting correlations (using BCS theory) for various regions of the parameter space formed by the interplanar variables. For $t_{\perp} = 0$ (confining the carriers in planes) and $J_{\perp} < J_{\parallel}$, the pairing correlations are found to be purely planar. Further we generalize to $t_{\perp} \ne 0$ and $J_{\perp}/J_{\parallel} = \left (t_{\perp}/t_{\parallel}\right )^{2}$ and find that pairing correlations are enhanced at lower densities with increasing $t_{\perp}$. The most dramatic effect sets in when, additionally the planar hopping frequencies are made highly anisotropic ($t_{y} \ll t_{x}$) and $J_{\perp} \sim J_{\parallel}$. A small $t_{\perp}$ increases $T_{c}$ as much as {\it {four}} times when compared with the calculations performed for a single layer (PRB, {\bf {66}}, 144507 (2002)). Straightforward generalizations to more number of layers is discussed with a goal to study crossover to the bulk 3D limit.