Effects of disorder range and electronic energy on the perfect transmission in graphene nanoribbons

Leandro R F Lima,Caio H Lewenkopf,Felipe A Pinheiro,Rodrigo B Capaz,Eduardo R Mucciolo

doi:10.1103/physrevb.86.205111

Abstract

Numerical calculations based on the recursive Green's functions method in the tight-binding approximation are performed to calculate the dimensionless conductance $g$ in disordered graphene nanoribbons with Gaussian scatterers. The influence of the transition from short- to long-ranged disorder on $g$ is studied as well as its effects on the formation of a perfectly conducting channel. We also investigate the dependence of electronic energy on the perfectly conducting channel. We propose and calculate a backscattering estimative in order to establish the connection between the perfectly conducting channel (with $g=1$) and the amount of intervalley scattering.

Highlights

The remarkable electronic transport properties of graphene have motivated numerous experimental and theoretical studies.1–3 Of particular interest is the possibility of fabricating narrow graphene samples, called graphene nanoribbons (GNRs)
We investigate the dependence of electronic energy on the perfectly conducting channel
For disordered zigzag GNRs, electronic scattering should mix valleys, leading to the suppression of transmission depending on d. We address this issue by establishing a connection between the perfectly conducting channel (PCC) and the backscattering mechanism, analyzing both the shortranged disorder (SRD) and long-ranged disorder (LRD) regimes

Summary

Introduction

The remarkable electronic transport properties of graphene have motivated numerous experimental and theoretical studies. Of particular interest is the possibility of fabricating narrow graphene samples, called graphene nanoribbons (GNRs). The remarkable electronic transport properties of graphene have motivated numerous experimental and theoretical studies.. Of particular interest is the possibility of fabricating narrow graphene samples, called graphene nanoribbons (GNRs). By engineering the lateral confinement one can, in principle, create an electronic energy gap leading to a semiconductor behavior that allows for the development of novel electronic nanodevices and applications.. The observation of conductance quantization in GNRs turned out to be more difficult than anticipated.. The reason is that the vast majority of GNR samples are produced by lithographic patterning, characterized by rough edges at the atomic scale.. Already at low concentrations, such defects can destroy conductance quantization.. Edge roughness may be largely suppressed in GNRs produced by unzipping singlewall carbon nanotubes.. Edge roughness may be largely suppressed in GNRs produced by unzipping singlewall carbon nanotubes.12–14 The latter are not free of bulk defects The observation of conductance quantization in GNRs turned out to be more difficult than anticipated. The reason is that the vast majority of GNR samples are produced by lithographic patterning, characterized by rough edges at the atomic scale. Already at low concentrations, such defects can destroy conductance quantization. Edge roughness may be largely suppressed in GNRs produced by unzipping singlewall carbon nanotubes. the latter are not free of bulk defects

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Conclusion