Edge Effect on Electronic Transport Properties of Graphene Nanoribbons and Presence of Perfectly Conducting Channel

TL;DR

This study reveals that zigzag graphene nanoribbons exhibit a perfectly conducting channel due to edge states and valley imbalance, with transport properties strongly influenced by impurity range and edge structure.

Contribution

It demonstrates the existence of a perfectly conducting channel in disordered zigzag nanoribbons and classifies their transport behavior based on impurity range and edge structure.

Findings

Perfectly conducting channel arises in zigzag ribbons with long-range impurities.

Short-range impurities lead to conventional localization behavior.

Chiral edge channels are present in various edge structures except armchair edges.

Abstract

Numerical calculations have been performed to elucidate unconventional electronic transport properties in disordered nanographene ribbons with zigzag edges (zigzag ribbons). The energy band structure of zigzag ribbons has two valleys that are well separated in momentum space, related to the two Dirac points of the graphene spectrum. The partial flat bands due to edge states make the imbalance between left- and right-going modes in each valley, {\it i.e.} appearance of a single chiral mode. This feature gives rise to a perfectly conducting channel in the disordered system, i.e. the average of conductance $<g>$ converges exponentially to 1 conductance quantum per spin with increasing system length, provided impurity scattering does not connect the two valleys, as is the case for long-range impurity potentials. Ribbons with short-range impurity potentials, however, through inter-valley scattering, display ordinary localization behavior. Symmetry considerations lead to the classification of disordered zigzag ribbons into the unitary class for long-range impurities, and the orthogonal class for short-range impurities. The electronic states of graphene nanoribbons with general edge structures are also discussed, and it is demonstrated that chiral channels due to the edge states are realized even in more general edge structures except for armchair edges.