Negative differential resistance in molecular junctions: application to   graphene ribbon junctions
  Using self-consistent calculations based on Non-Equilibrium Green's Function (NEGF) formalism, the origin of negative differential resistance (NDR) in molecular junctions and quantum wires is investigated. Coupling of the molecule to electrodes becomes asymmetric at high bias due to asymmetry between its highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) levels. This causes appearance of an asymmetric potential profile due to a depletion of charge and reduction of screening near the source electrode. With increasing bias, this sharp potential drop leads to an enhanced localization of the HOMO and LUMO states in different parts of the system. The reduction in overlap, caused by localization, results in a significant reduction in the transmission coefficient and current with increasing bias. An atomic chain connected to two Graphene ribbons was investigated to illustrate these effects. For a chain substituting a molecule, an even-odd effect is also observed in the NDR characteristics. 
Hosein Cheraghchi, Keivan Esfarjani