ELIASHBERG EQUATIONS AND SUPERCONDUCTIVITY IN A LAYERED 2-DIMENSIONALMETAL

The Eliashberg equations for superconductivity in a layered two-dimens ional (2D) metal, taking into account the interaction between an elect ron and an arbitrary boson excitation, are obtained. The theory is app lied to the case of a plasmon-mediated electron-electron interaction a nd it is shown that the interelectronic Coulomb repulsion parameter mu is connected with both the bare Coulomb interaction and the single-pa rticle excitation. An evaluation of this parameter shows that while re maining 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 renormaliz ation factor Z(omega) as omega-->0 and T-->0. This gives rise to a log arithmic dependence of lambda(pl), the electron-plasmon interaction co nstant, on temperature for T greater-than-or-equal-to T(c) and a logar ithmic 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 inte layer plasmon exchange, the cutoff frequency for plasmon exchange reac hes its maximum value at the Fermi energy epsilon(F), which leads to t he important conclusion that T(c) is proportional to epsilon(F)e-1/lam bdaeff.