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 the following. (i) Electrons accumulating along the edges of the uniform ribbon and along the 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 intrasubband scattering while the noninteracting electron theory predicts the predominance of intersubband 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 $2{e}^{2}/h$ conductance plateau for the cosine constriction than is found in the absence of electron interactions. Possible implications for recent experiments are briefly discussed.