Effect of electron-electron interactions on the electronic structure and conductance of graphene nanoconstrictions

Abstract

We present self-consistent calculations of electron transport in graphene nanoconstrictions within the Hartree approximation. We consider suspended armchair ribbons with V-shaped constrictions having perfect armchair or zigzag edges as well as mesoscopically smooth but atomically stepped constrictions with cosine profiles. Our calculations are based on a tight-binding model of the graphene and account for electron-electron interactions in both the constriction and the semi-infinite leads explicitly. We find that electron interactions result in (i) Electrons accumulating along edges of the uniform ribbon and along zigzag and cosine constriction edges but not along armchair constriction edges. (ii) The first subband showing almost perfect transmittance due to localization at the uniform graphene boundary except at low energies for the cases of zigzag and cosine constrictions where Bloch stop-bands form in related periodic structures. (iii) The second subband being almost perfectly blocked by the constriction. (iv) Electron interactions favor intra-subband scattering while the non-interacting electron theory predicts predominance of inter-subband scattering. (v) Conductance quantization for the first few conductance steps being more pronounced for armchair constrictions but less so for zigzag constrictions. (vi) A much more prominent 2e 2 /h conductance plateau for the cosine constriction than is found in the absence of electron interactions. Possible implications for recent experiments are briefly discussed. arXiv:1206.4287v1 [cond-mat.mes-hall]

Effect of edge reconstruction and electron-electron interactions on quantum transport in graphene nanoribbons

“…1,2 Finally we report on calculations with electron-electron interactions taken into account in the Hartree approximation for a representative class of systems with single and multiple heptagon defects in aGNRs. Consistent with previous studies, 17,18 we find the electron-electron interactions to give rise to charge redistribution towards the edges of the ribbons when gating shifts the ribbon Fermi energy away from the Dirac point. This results in enhanced concentrations of the charge carriers on the defects at the edges of the ribbon.…”

“…We consider suspended graphene nanoribbons, adopting a similar approach to that in Ref. 18. The GNR is separated from the back gate by dielectric and air layers and is attached at its two ends to semiinfinite leads represented by ideal ribbons having the same width W .…”

“…It has also been shown that electron-electron interactions modify electron conduction in GNRs substantially. 17,18 Specifically, when the electron Fermi level is not at the charge neutrality point, electrons are predicted to accumulate along the edges of the ribbon and therefore any edge imperfection may be expected to play an important role in transport. However, the interplay between this charge redistribution effect and edge reconstruction in the context of transport is yet to be examined either theoretically or experimentally.…”

Imaging backscattering in graphene quantum point contacts

“…In graphene the channel constriction by external gates is ineffective due to Klein tunneling [25]. Etched QPCs were studied instead by both experiment [26][27][28][29] and theory [30][31][32]. In bilayer graphene [33][34][35] it is possible to induce a bandgap by applying a bias between the layers [36][37][38].…”

Electron interaction, charging, and screening at grain boundaries in graphene

“…The conductance calculations with a self-consistent potential are performed on the basis of the Landauer formalism using the standard recursive Green's function technique as described in Ref. 30. The band structure calculations are performed in the ribbon geometry with the GB residing in the middle of the ribbon, which is infinite in the x direction and has a finite width of 20 nm in the transverse y direction.…”