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The Wannier - Stark effect in electrified tight-binding systems is investigated, via the recursive Green-function technique, which involves repeated use of the Dyson equation. Green functions for finite, semi-infinite and infinite systems are generated in the site representation in the form of continued fractions, which are then expressed analytically as ratios of Bessel functions. The local densities of states at the surface and in the bulk are presented and their dependence on the applied field discussed.

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The control of the transmission of electrons along a polyene chain by an impurity is studied. A semiconducting chain of atoms is modeled by a tight-binding Hamiltonian with alternating bonds into which the impurity is inserted. The energy-dependent transmission coefficient t and the change in the chain's electronic density of states are extracted from the transfer matrix across the impurity. The switching ability of the impurity is considered by altering either its site energy or one of its bonds with the conducting chain. Invoking the Joyce-Dixon approximation enables us to write the Azbel's energy-independent effective-transmission coefficient t,z, in a form where its Fermi level is temperature dependent, so that thermal effects can be investigated. The effects of site energy, impurity coupling, and bond ratio of both the impurity and chain are investigated by comparing their ability to alter the energy-averaged effective transmission coefficient as a function of either switching parameter to the ideal switcha step function.