Statistical electron-hole correlation in disordered systems: interband transitions

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Abstract
The dielectric response function is calculated exactly for transitions between a deep flat valence band and a conduction band with Lorentzian distribution of site levels (Lloyd's model). Site energies fluctuate independently of one another whereas the difference between the excited and the ground levels of each site is kept constant. Numerical examples are presented for three model densities of states. The effect of the fluctuations is to smear the edges and introduce small tails if the disorder is small. The absorption tail is much weaker than would be suggested by the tails in the densities of states. Large fluctuations of site energy levels reduce the density of states in the middle of the bands thus increasing the lifetime of the Wannier states, as a result the absorption band becomes narrower with increasing disorder.