Transmission through finite 1D barriers containing correlated impurities: an analytic formulation

We address the problem of electronic transmission through a finite sequence of identical potential barriers in one dimension, which has embedded in it “correlated impurities” that is, smaller identical clusters of n-mers, each described by n identical impurity potentials. Analytic formulae are derived for the transmission coefficient, and the investigation of Dunlap et al. [Phys. Rev. Lett. 65 (1990) 88], which were carried out for the corresponding dimer problem in the tight-binding model, are re-examined and generalised. The dependence of the condition for perfect transmission is obtained as a function of the strength of the impurity potential, treated here as a control parameter, in the case of a sequence of δ-function potentials.