Transport in single-molecule transistors: Kondo physics and negative differential resistance

We report two examples of transport phenomena based on sharp features in the effective density of states of molecular-scale transistors: Kondo physics in C$_{60}$-based devices, and gate-modulated negative differential resistance (NDR) in ``control'' devices that we ascribe to adsorbed contamination. We discuss the need for a statistical approach to device characterization, and the criteria that must be satisfied to infer that transport is based on single molecules. We describe apparent Kondo physics in C$_{60}$-based single-molecule transistors (SMTs), including signatures of molecular vibrations in the Kondo regime. Finally, we report gate-modulated NDR in devices made without intentional molecular components, and discuss possible origins of this property.