Rough edges in quantum transport of Dirac particles

TL;DR

This paper investigates how rough edges affect quantum transport in Dirac particles like graphene nanoribbons, revealing edge scattering's impact on conductivity and comparing Dirac and Schrödinger particles.

Contribution

It provides a perturbative analysis of edge scattering effects on conductivity in Dirac particles and compares these effects with Schrödinger particles.

Findings

Edge roughness causes transverse channel-mixing in Dirac particles.

Edge scattering significantly limits quantum transport in narrow ribbons.

Comparison shows differences between Dirac and Schrödinger particle transport.

Abstract

We consider Dirac particles confined to a thin strip, e.g., graphene nanoribbon, with rough edges. The confinement is implemented by a large mass in the Hamiltonian or by imposing boundary conditions directly on the graphene wave-functions. The scattering of a rough edge leads to a transverse channel-mixing and provides crucial limitation to the quantum transport in narrow ribbons. We solve the problem perturbatively and find the edge scattering contribution to the conductivity, which can be measured experimentally. The case of Schroedinger particles in a strip is also addressed, and the comparison between Schroedinger and Dirac transport is made. Anomalies associated with quasi-one dimensionality, such as Van Hove singularities and localization, are discussed. The violation of the Matthiessen rule is pointed out.