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Unusual properties of midband states in systems with off-diagonal disorder

1994; American Physical Society; Volume: 49; Issue: 5 Linguagem: Inglês

10.1103/physrevb.49.3190

1095-3795

M. Inui, S. A. Trugman, Elihu Abrahams,

Theoretical and Computational Physics

It is known that off-diagonal disorder results in anomalous localization at the band center, whereas diagonal disorder does not. We show that the important distinction is not between diagonal and off-diagonal disorder, but between bipartite and nonbipartite lattices. We prove that bipartite lattices in any dimension (and some generalizations that are not bipartite) have zero energy (i.e., band-center) eigenfunctions that vanish on one sublattice. We show that ln\ensuremath{\Vert}${\mathrm{\ensuremath{\psi}}}_{\mathit{j}}$\ensuremath{\Vert} has random-walk behavior for one-dimensional systems with first-, or first- and third-neighbor random hopping, leading to exp(-\ensuremath{\lambda} \ensuremath{\surd}r) localization of the zero-energy eigenfunction. Addition of diagonal disorder leads to a biased random walk. First- and second-neighbor random hopping with no diagonal disorder leads to ordinary exponential [exp(-\ensuremath{\lambda}r)] localization. Numerical simulations show anomalous localization in dimensions 1 and 2, with additional periodic structure in some cases.