  The quantum Hall effect in Graphene nano-ribbons (GNR) is investigated with
the non-equilibrium Green s function (NEGF) based quantum transport model in
the ballistic regime. The nearest neighbor tight-binding model based on pz
orbital constructs the device Hamiltonian. GNRs of different edge geometries
(Zigzag and Armchair) are considered. The magnetic field is included in both
the channels and contact through Peierls substitution. Efficient algorithms for
calculating the surface Green function are used to save computation time while
simulating realistically large dimensions comparable to those used in
experiments. Hall resistance calculations exactly reproduce the quantum Hall
plateaus observed in the experiments. Use of large dimensions in the simulation
is crucial in order to capture the quantum Hall effect in magnetic fields
within experimentally relevant 10-20T.
