Localization properties of one-dimensional random electrified chains

Abstract

A Kronig-Penney model with a constant electric field F for a non-interacting election is used to study the transmission properties of the Anderson transition in one-dimensional systems with disordered delta -function potentials. We examine the cases where the potential varies uniformly from 0 to W (barriers) or from -W to 0 (wells) for a given disorder W. We observe jumps in the transmission coefficient at the points E+Fx=n2 pi 2 (where E is the electron energy and n an integer). These jumps are related to the small oscillations observed by Soukoulis et al. in the mixed case (potentials from -W/2 to W/2). However, an interesting feature is found in the wells in the range between two jumps. It is observed that in the presence of a small field the states become more localized and the localization length decreases up to a minimum for a critical value Fm instead of increasing. Finally, we have studied the effect of the disorder on the Anderson transition by means of the participation ratio and the localization length.