Electronic transmission coefficient for the single-impurity problem in the scattering-matrix approach

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Abstract
The ability of a rupture of translational invariance in a one-dimensional chain to control the through chain electron propagation is studied on the model system ...AAABAAA... . A discrete formulation of the one-dimensional scattering theory is considered with the help of the transfer-matrix technique. A tight-binding Hamiltonian, with a single orbital per center, is used to represent the chemical nature of the perturbated chain. The electronic transmission coefficient and the change in the chain electronic density of states induced by the defect B are analytically calculated from the scattering matrix S. The complete dependence on the electronic transmission of the energetic position of the impurity orbital and of its couplings with the chain is analyzed in detail. Possible applications of the model to the design of molecular switches are described by means of the effective Azbel’s transmission coefficient.