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 by-height and 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.

Statistical properties of wave transport through surface-disordered waveguides

“…This expression is similar to that obtained for chaotic cavities (see equations [76], [93] in [109]). In another context, equation (41) would correspond to the exact RMT distribution for randomly coupled wide-narrow-wide leads [108].…”

“…The peculiar properties of transport through surface disordered waveguides have motivated an increasing theoretical interest in the study of different statistical aspects of the problem during the last few years [84][85][86][87][88][89][90][91][92][93][94][95][96][97][98]. The analysis of these complex statistical problems usually requires the use of powerful numerical methods.…”

One-particle conductance of an open quasi-two-dimensional Fermi system: Evidence of the parallel-magnetic-field-induced mode reduction effect

“…[14,46,47]. It relies basically on the fact that under WS conditions the functional arguments (A.5) can be regarded as Gaussiandistributed random variables [48].…”

Coexistence of Anderson and geometric-type localization of current carriers in multimode wires with surface disorder

“…This factor manifests itself in diverse phenomena such as Aharonov-Bohm and quantum Hall effects, non-homogeneous concentration of energy in randomly filled cavities [2], unusual properties of current carrier transport in wires both with isolated bends (in Ref. [3], the "bent resistance" has been detected experimentally) and in ballistic conductors with randomly distorted boundaries [4]- [6].…”

“…Similar problem was solved previously in Refs. [5], [6], where the one-mode metal strip was considered, which, to a certain accuracy, can be regarded as a strictly 1D disordered quantum system. According to the general theory of such systems, all the electron states in that strip were proven to be exponentially localized at an arbitrary level of boundary roughness.…”