Generalized transfer matrix theory on electronic transport through graphene waveguide

TL;DR

This paper develops a generalized transfer matrix method to analyze electronic transport in graphene waveguides, revealing an insulating band due to antiresonance effects that can be tuned by a gate voltage, with potential device applications.

Contribution

It introduces a generalized transfer matrix approach for complex graphene waveguides, extending beyond tight-binding methods, and demonstrates its effectiveness in predicting conductance features.

Findings

The graphene waveguide shows a well-defined insulating band around the Dirac point.

The insulating band results from antiresonance effects related to edge states.

The insulating band can be shifted by a gate voltage, enabling device applications.

Abstract

In the effective mass approximation, electronic property in graphene can be characterized by the relativistic Dirac equation. Within such a continuum model we investigate the electronic transport through graphene waveguides formed by connecting multiple segments of armchair-edged graphene nanoribbons of different widths. By using appropriate wavefunction connection conditions at the junction interfaces, we generalize the conventional transfer matrix approach to formulate the linear conductance of the graphene waveguide in terms of the structure parameters and the incident electron energy. In comparison with the tight-binding calculation, we find that the generalized transfer matrix method works well in calculating the conductance spectrum of a graphene waveguide even with a complicated structure and relatively large size. The calculated conductance spectrum indicates that the graphene waveguide exhibits a well-defined insulating band around the Dirac point, even though all the constituent ribbon segments are gapless. We attribute the occurrence of the insulating band to the antiresonance effect which is intimately associated with the edge states localized at the shoulder regions of the junctions. Furthermore, such an insulating band can be sensitively shifted by a gate voltage, which suggests a device application of the graphene waveguide as an electric nanoswitch.