  The effect of electric field, applied on systems in the nanoscale regime has
attracted a lot of research in recent times. We highlight some of the recent
results in the field of single molecule electronics and then move on to focus
on some of our own results in this area. We have first shown how important it
is to obtain the spatial profile of the external bias potential across the
system, and how this would change in the presence of electron-electron
interactions. We have also studied different kinds of insulators in the
presence of the spatially varying external bias, and have explicitly shown that
a two sublattice structure, caused either by a lattice distortion, or by the
presence of substituents with strong dipolar nature, can result in negative
differential resistance (NDR) in the transport characteristics. We also find
this to be true in case of correlated insulators. Additionally, we have shown
clear NDR behavior in a correlated double quantum dot by tuning the
electron-electron interaction strength in the system.
