Rough surface scattering in many-mode conducting channels: Gradient versus amplitude scattering

TL;DR

This paper investigates how surface roughness affects electron wave transport in multi-mode conducting channels, highlighting the importance of two control parameters, including a often-overlooked derivative mean, for understanding scattering behavior.

Contribution

It introduces a new control parameter based on the mean derivative of surface profiles, expanding the understanding of surface scattering effects in waveguides.

Findings

Two independent control parameters determine scattering properties.

The mean derivative of the surface profile can significantly influence scattering.

Results applicable to electron, optical, and microwave waveguides.

Abstract

We study the effect of surface scattering on transport properties in many-mode conducting channels (electron waveguides). Assuming a strong roughness of the surface profiles, we show that there are two independent control parameters that determine statistical properties of the scattering. The first parameter is the ratio of the amplitude of the roughness to the transverse width of the waveguide. The second one, which is typically omitted, is determined by the mean value of the derivative of the profile. This parameter may be large, thus leading to specific properties of scattering. Our results may be used in experimental realizations of the surface scattering of electron waves, as well as for other applications (e.g., for optical and microwave waveguides)