Off-diagonal disorder in one-dimensional systems

Abstract

We examine the nature of the zero-energy state in a one-dimensional tight-binding system with only nearest-neighbor off-diagonal disorder. We find that, although the localization length diverges at this energy, the state must nevertheless be considered as localized because the mean values of the transmission coefficient (which is directly related with the dc conductance) approach zero as the size of the system $L$ goes to infinity. In particular, we find that the geometric and harmonic mean values of the transmission coefficient behave as $\mathrm{exp}(\ensuremath{-}\ensuremath{\gamma}\sqrt{L})$, while the arithmetic mean value follows the power law ${L}^{\ensuremath{-}\ensuremath{\delta}}$ with $\ensuremath{\delta}\ensuremath{\simeq}0.50$. This is in contrast with the usual case of only diagonal disorder, where all three means behave as $\mathrm{exp}(\ensuremath{-}\ensuremath{\lambda}L)$.