  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.
