Phonon-mediated negative differential conductance in molecular quantum dots

Transport through a single-molecular conductor is considered, showing negative differential conductance behavior associated with phonon-mediated electron tunneling processes. This theoretical work is motivated by a recent experiment by Leroy using a carbon nanotube contacted by a scanning tunneling microscope tip [Nature 432, 371 (2004)], where negative differential conductance of the breathing-mode phonon side peaks could be observed. A peculiarity of this system is that the tunneling couplings which inject electrons and those which collect them on the substrate are highly asymmetrical. A quantum dot model is used, coupling a single electronic level to a local phonon, forming polaron levels. A "half-shuttle" mechanism is also introduced. A quantum kinetic formulation allows us to derive rate equations. Assuming asymmetric tunneling rates and in the absence of the half-shuttle coupling, negative differential conductance (NDC) is obtained for a wide range of parameters. A detailed explanation of this phenomenon is provided, showing that NDC is maximal for intermediate electron-phonon coupling. In addition, in the absence of a gate, the "floating" level results in two distinct lengths for the current plateaus, related to the capacitive couplings at the two junctions. It is shown that the half-shuttle mechanism tends to reinforce the negative differential regions, but it cannot trigger this behavior on its own.