Density-functional method for the inhomogeneous electron-hole plasma in polar substances

The density-functional method is shown to be applicable to an inhomogeneous electron-hole plasma too, if all charged particles interact strongly with LO-phonons. Especially, the expectation value of the lattice polarization is proven to be independent of the dynamic interaction processes between particles and phonons. It only depends on the electronic charge densities, and, therefore, the energy is a functional of ne and nh alone. The influence of the particle-phonon interaction on the Hartree-contributions of the energy functional consists solely in the change of the screening constant from ϵ∞ to ϵ0. Integrating over a coupling constant the exchange-correlation part Exc of the energy functional can be expressed by the longitudinal inverse dielectric function ϵ-11 (r, r′, ω) of the considered inhomogeneous system. It is remarkable that only the diagonal part (r = r') of this function is needed. There exists the possibility to obtain a tractable expression for Exc in the local density approximation (LDA) possessing the same high quality as in the case without particle-phonon interaction. In order to determine the electronic charge densities self-consistent one-particle equations (Kohn-Sham equations) are derived. Adopting LDA the influence of particle-phonon interaction is shown to yield renormalization of charged particles to polarons and effective density-dependent screening of the exchange contribution. The presented approach can be used to obtain information, e.g., about the stability of bound multiexciton complexes in polar semiconductors.