Phonon-mediated negative differential conductance in molecular quantum dots

TL;DR

This paper presents a theoretical study of phonon-mediated negative differential conductance in molecular quantum dots, explaining experimental observations and identifying key mechanisms like asymmetrical tunneling and electron-phonon coupling.

Contribution

It introduces a quantum kinetic model incorporating asymmetrical tunneling and a half-shuttle mechanism to explain NDC in molecular conductors, extending understanding of phonon effects in quantum dots.

Findings

Negative differential conductance occurs for a wide range of parameters.

NDC is maximized at intermediate electron-phonon coupling.

The half-shuttle mechanism reinforces but does not trigger NDC.

Abstract

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 et al. using a carbon nanotube contacted by an STM tip [Nature {\bf 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 to derive rate equations. Assuming asymmetric tunneling rates, and in the absence of the half-shuttle coupling, negative differential conductance 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 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.