Collective Excitations and Superconductivity in Reduced Dimensional Systems-Possible Mechanism for High -T

We study in full detail a possible mechanism of superconductivity in slender electronic systems of finite cross section. This mechanism is based on the pairing interaction mediated by the multiple modes of acoustic plasmons in these structures. First, we show that multiple non-Landau-damped acoustic plasmon modes exist for electrons in a quasi-one dimensional wire at finite temperatures. These plasmons are of two basic types. The first one is made up by the collective longitudinal oscillations of the electrons essentially of a given transverse energy level oscillating against the electrons in the neighboring transverse energy level. The modes are called Slender Acoustic Plasmons or SAP's. The other mode is the quasi-one dimensional acoustic plasmon mode in which all the electrons oscillate together in phase among themselves but out of phase against the positive ion background. We show numerically and argue physically that even for a temperature comparable to the mode separation Deltaomega the SAP's and the quasi-one dimensional plasmon persist. Then, based on a clear physical picture, we develop in terms of the dielectric function a theory of superconductivity capable of treating the simultaneous participation of multiple bosonic modes that mediate the pairing interaction. The effect of mode damping is then incorporated in a simple manner that is free of the encumbrance of the strong-coupling, Green's function formalism usually required for the retardation effect. Explicit formulae including such damping are derived for the critical temperature T_ c and the energy gap Delta_0. With those modes and armed with such a formalism, we proceed to investigate a possible superconducting mechanism for high T_ c in quasi-one dimensional single-wire and multi-wire systems. Due to the small mass of the electrons and the effective plasmon frequency, the electron-electron coupling strength and therefore T _ c are enhanced in these systems. Numerical examples show T_ c in the 200 K range for both systems. However, the critical temperature of the multi-wire is enhanced over the critical temperature of the single-wire system. This fact stems from the in -phase wire-wire Coulomb coupling. Finally we present general conclusions and point out the various ways in which this work could be further studied and expanded.