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We study the conductance through two types of graphene nanostructures: nanoribbon junctions in which the width changes from wide to narrow, and curved nanoribbons. In the wide-narrow structures, substantial reflection occurs from the wide-narrow interface, in contrast to the behavior of the much studied electron gas waveguides. In the curved nanoribbons, the conductance is very sensitive to details such as whether regions of a semiconducting armchair nanoribbon are included in the curved structure -- such regions strongly suppress the conductance. Surprisingly, this suppression is not due to the band gap of the semiconducting nanoribbon, but is linked to the valley degree of freedom. Though we study these effects in the simplest contexts, they can be expected to occur for more complicated structures, and we show results for rings as well. We conclude that experience from electron gas waveguides does not carry over to graphene nanostructures. The interior interfaces causing extra scattering result from the extra effective degrees of freedom of the graphene structure, namely the valley and sublattice pseudospins.
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We report on the observation of periodic conductance oscillations near quantum Hall plateaus in suspended graphene nanoribbons. They are attributed to single quantum dots that form in the narrowest part of the ribbon, in the valleys and hills of a disorder potential. In a wide flake with two gates, a double-dot systems signature has been observed. Electrostatic confinement is enabled in single-layer graphene due to the gaps that form between Landau levels, suggesting a way to create gate-defined quantum dots that can be accessed with quantum Hall edge states.
We report the experimental observation of conductance quantization in graphene nanoribbons, where 1D transport subbands are formed due to the lateral quantum confinement. We show that this quantization in graphene nanoribbons can be observed at temperatures as high as 80 K and channel lengths as long as 1.7 $mu$m. The observed quantization is in agreement with that predicted by theoretical calculations.
We study Andreev reflection in graphene nanoribbon/superconductor hybrid junctions. By using a tight-binding approach and the scattering formalism we show that finite-size effects lead to notable differences with respect to the bulk graphene case. At subgap voltages, conservation of pseudoparity, a quantum number characterizing the ribbon states, yields either a suppression of Andreev reflection when the ribbon has an even number of sites in the transverse direction or perfect Andreev reflection when the ribbon has an odd number of sites. In the former case the suppression of Andreev reflection induces an insulating behavior even when the junction is biased; electron conduction can however be restored by applying a gate voltage.
A theoretical study of the transport properties of zigzag and armchair graphene nanoribbons with a magnetic barrier on top is presented. The magnetic barrier modifies the energy spectrum of the nanoribbons locally, which results in an energy shift of the conductance steps towards higher energies. The magnetic barrier also induces Fabry-Perot type oscillations, provided the edges of the barrier are sufficiently sharp. The lowest propagating state present in zigzag and metallic armchair nanoribbons prevent confinement of the charge carriers by the magnetic barrier. Disordered edges in nanoribbons tend to localize the lowest propagating state, which get delocalized in the magnetic barrier region. Thus, in sharp contrast to the case of two-dimensional graphene, the charge carriers in graphene nanoribbons cannot be confined by magnetic barriers. We also present a novel method based on the Greens function technique for the calculation of the magnetosubband structure, Bloch states and magnetoconductance of the graphene nanoribbons in a perpendicular magnetic field. Utilization of this method greatly facilitates the conductance calculations, because, in contrast to excising methods, the present method does not require self-consistent calculations for the surface Greens function.
We propose that recent transport experiments revealing the existence of an energy gap in graphene nanoribbons may be understood in terms of Coulomb blockade. Electron interactions play a decisive role at the quantum dots which form due to the presence of necks arising from the roughness of the graphene edge. With the average transmission as the only fitting parameter, our theory shows good agreement with the experimental data.
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