Reflectionless modes in chains with large-size homogeneous impurities

Abstract

The authors study the spectra and localization properties of tight-binding chains with randomly distributed binary blocks of arbitrary size m; one having site energies epsilon _A and the other epsilon _B, respectively. They demonstrate that for block size m greater than one and delta = mod epsilon _A- epsilon _B less than a critical value delta _c(m) perfect transmission resonance modes exist in the band. Their number is proportional to m and they occur via dominant 1/E² divergencies of the localization length. No transmission is found for delta > delta _c(m). The results are understood by solving exactly the scattering problem from a single homogeneous impurity block of arbitrary size m. In the limit of hard impurities (m to infinity ) transmission stops only when delta > delta _c( infinity )=4V, V being the intersite matrix element; that is when the pure A and B bands become detached.