Atomistic Non-equilibrium Green s Function Simulations of Graphene Nano-Ribbons in the Quantum Hall Regime

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.