Density of states and superconducting phase boundary for model systems

Analytic expressions for the exact Green's functions for electrons and phonons in a bimetallic superlattice are obtained. The electrons are treated in the tight-binding approximation, and the phonons are of one acoustic branch in a lattice with nearest-neighbor coupling. The most interesting effects arise near the interfaces when the acoustical or electronic coupling between layers is large compared to the intralayer coupling. In this large coupling case, the local phonon density of states at low frequency is enhanced by a linear contribution due to interface modes. The appearance of electronic interface states in the local density of states is discussed. The impact of these results on superconducting properties is considered. The influence of zone-folding effects is found to be small. The superconducting critical temperature, T/sub c/, of a bimetallic superlattice is then investigated. It is found that T/sub c/ is enhanced above the Cooper limit because of the influence of periodicity on the order parameter in the system. This system is discussed by using the simple analogy between the Ginzburg-Landau equation for the order parameter near the phase boundary and the Schroedinger equation for an electron in a quasi-one-dimensional periodic potential. A magnetic field is then introduced in the problem and the phase boundary is obtained for the case of fields parallel and perpendicular to the layers. For arbitrarily oriented fields, the variation of the upper critical field, H/sub c2/, with angle is observed. The result shows anisotropic behavior