REFLECTIONLESS MODES IN CHAINS WITH LARGE-SIZE HOMOGENEOUS IMPURITIES

We study the spectral 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. We demonstrate that for block size m greater than one and delta = \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). Our 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 --> 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.