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A first-principles calculation of the impurity screening in Si and Ge nanocrystals is presented. We show that isocoric screening gives results in agreement with both the linear response and the point-charge approximations. Based on the present ab initio results, and by comparison with previous calculations, we propose a physical real-space interpretation of the several contributions to the screening. Combining the Thomas-Fermi theory and simple electrostatics, we show that it is possible to construct a model screening function that has the merit of being of simple physical interpretation. The main point upon which the model is based is that, up to distances of the order of a bond length from the perturbation, the charge response does not depend on the nanocrystal size. We show in a very clear way that the link between the screening at the nanoscale and in the bulk is given by the surface polarization. A detailed discussion is devoted to the importance of local field effects in the screening. Our first-principles calculations and the Thomas-Fermi theory clearly show that in Si and Ge nanocrystals, local field effects are dominated by surface polarization, which causes a reduction of the screening in going from the bulk down to the nanoscale. Finally, the model screening function is compared with recent state-of-the-art ab initio calculations and tested with impurity activation energies.

We calculate the influence of dynamical exchange effects on the response properties and the static properties of a two-dimensional many-polaron gas. These effects are not manifested in the random-phase approximation which is widely used in the analysis of the many-polaron system. Here they are taken into account by using a dielectric function derived in the time-dependent Hartree-Fock formalism. At weak electron-phonon coupling, we find that dynamical exchange effects lead to substantial corrections to the random-phase approximation results for the ground state energy, the effective mass, and the optical conductivity of the polaron system. Furthermore, we show that the reduction of the spectral weight of the optical absorption spectrum at frequencies above the longitudinal optical phonon frequency, due to many-body effects, is overestimated by the random-phase approximation., Comment: 9 pages, 7 figures