Electron localization in narrow surface-corrugated conducting channels: Manifestation of competing scattering mechanisms

Abstract

Transport properties of narrow two-dimensional conducting wires in which the electron scattering is caused by side edges' roughness have been studied. The method for calculating dynamic characteristics of such conductors is proposed which is based on the two-scale representation of the mode wave functions at weak scattering. With this method, fundamentally different {\it by-height} and {\it by-slope} scattering mechanisms associated with edge roughness are discriminated. The results for single-mode systems, previously obtained by conventional methods, are proven to correspond to the former mechanism only. Yet the commonly ignored by-slope scattering is more likely dominant. The electron extinction lengths relevant to this scattering differ substantially in functional structure from those pertinent to the by-height scattering. The transmittance of ultra-quantum wires is calculated over all range of scattering parameters, from ballistic to localized transport of quasi-particles. The obtained dependence of scattering lengths on the disorder parameters is valid qualitatively for arbitrary inter-correlation of the boundaries' defects.