Insulator-metal transitions in random lattices containing symmetrical defects

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Abstract
We show in this paper, within the context of a tight-binding model, that when defects spanning more than one lattice size contain a plane of symmetry, the standard tendency of disorder to localize electronic states can be suppressed at certain energies in the band. A general transfer-matrix approach is used to show exactly that when such defects are sprinkled at random on a linear chain, √N (N is the number of states) of the electronic states will remain unscattered by the disorder regardless of the concentration of the defects. The location in the energy band of the unscattered states is determined by the unit transmission condition for a single defect. The delocalization-localization transition recently reported in a series of one-dimensional models, such as the random-dimer model, is shown to result from the general condition of symmetric internal structure. We demonstrate that the continuum limit of these models is simply a collection of randomly placed square barriers (or wells) on a line and show that regardless of the distribution of separations between the barriers, √N of the electronic states in the vicinity of the zero-reflectance condition will necessarily be extended.