Dual nature of localization in guiding systems with randomly corrugated boundaries: Anderson-type versus entropic

TL;DR

This paper develops a unified theory describing how boundary roughness in quantum wires causes different types of wave scattering and localization, revealing the coexistence of entropic and Anderson localization mechanisms.

Contribution

It introduces a comprehensive framework that accounts for all scattering mechanisms in randomly corrugated quantum wires, highlighting the dual nature of localization phenomena.

Findings

Boundary roughness acts as a mode-specific effective potential barrier.

Two localization types coexist: entropic and Anderson localization.

Strong intermode scattering leads to decoupled extended modes.

Abstract

A unified theory for the conductance of a long multimode quantum wire whose finite segment has randomly rough boundaries is developed. It enables one to take account of all mechanisms of wave scattering, both related to boundary roughness and to contacts between the wire rough section and the leads within the same technical frameworks. The rough part of the conducting wire is shown to act as a mode-specific randomly modulated effective potential barrier whose height is governed essentially by the asperity slope. The mean height of the barrier specifies the number of conducting channels. Under relatively small asperity amplitude this number can take on arbitrary small values if the asperities are sufficiently sharp. The channel cut-off that arises when the asperity sharpness increases can be regarded as a kind of localization, which is not related to the disorder but rather is of entropic origin. The fluctuating part of the barrier results in two fundamentally different types of guided wave scattering, viz., inter- and intramode scattering. The intermode scattering is shown to be for the most part very strong except in the cases of (a) extremely smooth asperities, (b) excessively small length of the corrugated segment, and (c) the asperities sharp enough for only one conducting channel to remain in the wire. Under strong intermode scattering, a new set of conducting channels develops, which have the form of decoupled extended modes subject to individual random potentials. In view of this fact, two transport regimes only are realizable in randomly corrugated multimode wires, specifically, the ballistic and the localized regime, the latter characteristic of one-dimensional random systems. Two kinds of localization are thus shown to coexist in waveguide-like systems with randomly corrugated boundaries, specifically, the entropic localization and the one-dimensional Anderson localization.