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We present the results of million-atom electronic quantum transport calculations for graphene nanoconstrictions with edges that are smooth apart from atomic-scale steps. We find conductances quantized in integer multiples of 2e2/h and a plateau at ∼0.5 x 2e2/h as in recent experiments [N. Tombros et al, Nat. Phys. 7, 697 (2011)]. We demonstrate that, surprisingly, conductances quantized in integer multiples of 2e2/ h occur even for strongly nonadiabatic electron backscattering at the stepped edges that lowers the conductance by one or more conductance quanta below the adiabatic value. We also show that conductance plateaus near 0.5 x 2e2/ h can occur as a result of electron backscattering at stepped edges even in the absence of electron-electron interactions. [ABSTRACT FROM AUTHOR]

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 2e²/h conductance plateau for the cosine constriction than is found in the absence of electron interactions. Possible implications for recent experiments are briefly discussed. [ABSTRACT FROM AUTHOR]