ELIASHBERG EQUATIONS AND SUPERCONDUCTIVITY IN A LAYERED 2-DIMENSIONAL METAL

The Eliashberg equations for superconductivity in a layered two-dimensional (2D) metal, taking into account the interaction between an electron and an arbitrary boson excitation, are obtained. The theory is applied to the case of a plasmon-mediated electron-electron interaction and it is shown that the interelectronic Coulomb repulsion parameter mu is connected with both the bare Coulomb interaction and the single-particle excitation. An evaluation of this parameter shows that while remaining always positive, it decays with the decrease of the interlayer distance. It is also shown that the electron-plasmon interaction in a layered 2D system leads to a logarithmic divergence of the renormalization factor Z(omega) as omega-->0 and T-->0. This gives rise to a logarithmic dependence of lambda(pl), the electron-plasmon interaction constant, on temperature for T greater-than-or-equal-to T(c) and a logarithmic dependence on the gap parameter DELTA for T much less than T(c). It is found that at small interlayer distance, i.e., for strong intelayer plasmon exchange, the cutoff frequency for plasmon exchange reaches its maximum value at the Fermi energy epsilon(F), which leads to the important conclusion that T(c) is proportional to epsilon(F)e-1/lambdaeff.