Collective Modes, Effective Interaction and Superconductivity in the Electron-Hole Liquid.

Under favourable conditions a collective mode of the acoustic kind can exist in a degenerate electron -hole liquid (EHL). The dispersion and damping of such a mode in a model semiconductor are calculated within a generalized random-phase approximation. It is found that exchange and correlation reduce the phase velocity of the mode, increase its relative width and decrease the maximum wavevector beyond which it cannot propagate. In order to examine the possibility of superconductivity in an EHL a simple expression for the effective two-body interaction in a Fermi liquid whose constituents interact via a Coulomb force is derived on the basis of a diagrammatic analysis. The interaction, which is spin-dependent, is expressed in terms of local field factors and Lindhard polarizability. It is local in character (i.e. depends only on momentum and energy transfer) and includes the contribution of density and spin fluctuations both longitudinal and transverse. A comparison with other interactions known in the literature is presented. Using the two-component generalization of the effective electron-electron interaction it is shown that the EHL can become superconducting. The intermediate bosons responsible for superconducting pairing are not acoustic plasmons but correlated pair excitations from the Fermi sea of the holes. There is a large density of such excitations because the system is near to a compressional instability. The fact that they are strongly coupled to electrons follows from the specific form of the interaction, which includes vertex corrections and multiple electron -hole scattering. Some materials are shown to have EHL's with reasonably high transition temperatures (T(,c)(TURN)1('0)K) and are proposed for an experimental verification of the new mechanism of superconductivity. The transition temperature increases with decreasing density and with increasing mass ratio. Finally, the effect of superconductivity on acoustic plasmons is considered. In the extreme long wavelength limit a collisionless mode exists inside the energy gap for mass ratio > 5. It is not Landau-damped and its observation can provide evidence for superconductivity in the EHL.