Eliashberg equations and superconductivity in a layered two-dimensional metal

Abstract

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 μ 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(ω) as ω→0 and T→0. This gives rise to a logarithmic dependence of λpl, the electron-plasmon interaction constant, on temperature for T≥Tc and a logarithmic dependence on the gap parameter Δ for T≪Tc. 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 ɛF, which leads to the important conclusion that Tc is proportional to ɛFeeff−1/λ.

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