LOCALIZATION, ANTILOCALIZATION, AND DELOCALIZATION IN ONE-DIMENSIONAL DISORDERED LATTICES

We study analytically the eigenstates of a weakly disordered semi-infinite single-band tight-binding lattice in contact with an ordered parent lattice. We consider successively three simple types of correlated, continuously distributed site energies: a random dimer model, a random trimer model, and a random monomer-dimer model. In the dimer model the disordered chain lattice is partitioned into a collection of pairs of nearest-neighbor sites, where the two sites of a given pair are assigned a common independent random energy. The trimer model is similarly made up of triplets of nearest-neighbor sites having the same site energy taken as an independent random variable. Finally, the monomer-dimer model is defined as an alternate sequence of independent dimers and monomers with identically distributed site energies. The site energy randomness is described by Gaussian white noise and we restrict to energies of the pure systems energy band. We find that the averaged rates of exponential variation of site wave functions at finite distances N 1 from the edge site of the disordered chain are anomalous at the band center (E=0), at the band edges, and at energies E=2cos, with =1/4 for the dimer model and =1/6 1/3, 2/3, and 5/6 for the trimer and monomer-dimer models. These results are relevant for transport behavior of finite disordered samples in the quasimetallic regime. On the other hand, we study the inverse localization lengths for the states whose energies are intermediate to the above special values. In the dimer model all the states in this energy range are localized, with an enhanced localization length. In the trimer and monomer-dimer models we obtain six delocalized states at fixed intermediate energies. The energies of the delocalized states separate domains where all states are localized from domains where all states are antilocalized. The antilocalized states discussed in this paper have the usual Bloch form up to the edge site of the ordered lattice, beyond which they decrease exponentially into the disordered lattice. We also study the effect of disorder on the phase of site wave functions. © 1995 The American Physical Society.