Nonlocal dielectric susceptibility of a semi-infinite insulator

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Abstract
The excitonic contribution to the dielectric susceptibility of a semi-infinite simple cubic semiconductor bounded by a (001) surface is calculated in the tight-binding approximation. The electron and hole hopping integrals in the Hamiltonian for the system couple only nearest-neighbor sites, and the Coulomb interaction between the electron and hole occurs at a single site. A pair of free surfaces is created in an infinitely extended crystal by setting to zero the electron and hole hopping integrals connecting sites on opposite sides of a fictitious plane normal to the [001] direction, but containing no atoms itself. The integral equation for the two-particle Green's function in terms of which the susceptibility is expressed is solved analytically for frequencies in the excitonic regime. The dispersion relation for surface excitons is obtained, and the spatial variation of the polarization in the crystal induced by a spatially uniform macroscopic field is determined from our results.