Model for an exciton mechanism of superconductivity in planar geometry

The possibility of an exciton mechanism of superconductivity in planar geometry is investigated. Upon specialization to the case of the single interface between a thin, crystalline metal film in intimate contact with a clean semiconductor substrate, a model is developed in which the metal electrons with energies near the Fermi surface penetrate a short distance into the semiconductor. There they scatter by producing and absorbing virtual electron-hole pairs. The effect of such semiconductor polarization processes (i.e., the exciton mechanism) on the electron-electron interaction is estimated by two separate means and is found to lead to an attractive interaction for favorable choices of semiconductor and metal materials. A brief look at attempts to derive these results in terms of the microscopic dielectric function is also given. A calculation of what superconducting transition temperatures one could expect to see due to this effect follows, both for the case of the exciton mechanism acting alone, and for the case of the exciton mechanism combined with the usual phonon mechanisms. It is concluded that although the exciton mechanism has not yet been established experimentally, the theory has a sound physical basis and indicates that the effect of the exciton mechanism ought to be observable in favorable samples with sufficient effort. The immediate need is to fabricate such systems and establish the existence of the exciton mechanisms of superconductivity. (auth)