Beyond exponential localization in one-dimensional electrified chains

Abstract

We interpret a new kind of localization in a finite one-dimensional tight-binding model under a weak applied electric field. This phenomenon is quite general and manifests itself in a more than exponential decreasing behaviour of the chain transmittivity. We provide analytic expressions for the transmittivity and confirm the theoretical results by transfer matrix numerical calculations. We show that this phenomenon is present in ordered as well as in aperiodic (incommensurate and pseudorandom systems) irrespective of the number of allowed bands.

Electric-field effect on the transmittivity of aperiodic Kronig-Penney crystals

“…In fact, in the case of a single band we soon realize that, due to the slope of the allowed band, the distance of the given energy E from the band as a function of the length of the sample increases, determining the more than exponential decrease of transmittivity. 29 This effect does not occur in the absence of electric field because a forbidden energy has in real space a constant distance from the allowed band and therefore the transmittivity has a constant exponential decreasing rate.…”