Conductance footprints of impurity scattering in graphene nanoribbons

TL;DR

This paper analytically investigates how impurity scattering affects conductance in graphene nanoribbons, revealing how impurity location and type influence conductance resonances and transparency, with implications for nanoscale electronic transport.

Contribution

It provides a detailed analytical model of impurity scattering effects on conductance in graphene nanoribbons, including a generalized Fisher-Lee formula for graphene leads.

Findings

A-site impurities cause conductance dips or transparency at subband bottoms.

A-B-site impurities always reduce conductance steps due to sublattice scattering.

Conductance dips depend on impurity strength and doping type.

Abstract

We report a detailed analytic investigation of the interplay between size quantization and local scattering centers in armchair graphene nanoribbons, as seen in the conductance. The scattering property of a local scattering center is dependent on if it is located on one sublattice (A-site impurity) or both (impurity situated at neighboring carbon atoms, A-B-site impurity). The A-site impurity scatters in a similar way as a localized impurity in a one-dimensional channel made from a two-dimensional electron gas. On the other hand, the A-B-site impurity introduces A- to B-sublattice scattering, which knows about the chirality of Dirac electrons, and heavily influence the conductance. For A-site impurities, interplay between evanescent waves at the impurity and the propagating modes contributing to the conductance, leads to scattering resonances that generate either dips in the conductance or render the impurity completely transparent. The latter occurs at subband bottom energies where the wave vector of the opening mode is zero. The conductance of defect free graphene therefore remains at these energies. This is analagous to the case of a scattering center in a quantum channel made from a two-dimensional electron gas. The conductance dips occur at energies $\Delta E$ away from the conductance steps and their location depend directly on the impurity strength. In particular, for repulsive impurities the dips occur for hole-doping, while for attractive impurities for electron doping. For an A-B-site impurity, the A- to B-sublattice scattering interferes with the transmission resonance at the energies of the subband bottoms and the impurity is never transparent and the conductance steps of defect free graphene ribbons are always lost. We derive a generalized Fisher-Lee formula for graphene leads that holds for arbitrary scattering region and arbitrary number of leads.