Tunneling Enhancement of the Superconducting Transition Temperature

The observed \tc enhancement in heterostructures of high-temperature superconductors is investigated. The model assumes a two-layer system; a metallic layer providing large carrier concentration, (a charge-transfer layer), and a pairing layer, providing the order parameter, with a single-particle tunneling term. The model is solved within the mean-field approximation for the order parameter, but exactly by means of the functional integral formalism for the effect of the interlayer hopping term, $t_{\bot}.$. We are able to show, analytically, the dependence of major quantities on the interlayer hopping term. Pre-existing fermion pairs, which develop at $T_{MF}$, develop phase coherence and condense into a superfluid phase at a lower temperature, determined by the effective Kosterlitz-Thoulless hamiltonian, whose form we derive, and calculate numerically, the value of the transition temperature as a funtion of the interlayer hopping parameter $t_{\bot}.$ There is enhancement of the superconducting temperature for all values of the pairing layer Coulomb coupling, $\mathit{U},$ but this enhancement is non-monotonic with $t_{\bot}$ for large and intermediate coupling values, while it exhibits monotonicity in the low (Coulomb) coupling regime. This is found to be true for a wide range of fermionic densities. The \emph{BCS} ratio, that is the ratio of (twice) the gap in the energy spectrum at T=0, or ground state, to the mean field transition temperature, shows a monotonic departure from the BCS value of 3.5, with increasing $t_{\bot}.$Physics, Department o