  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.
