Vibration-assisted co-tunneling through single molecules

Prof. Dr. Herbert Schoeller, Dr. Maarten Rolf Wegewijs and Msc. Martin Leijnse,  Rheinisch-Westfälische Technische Hochschule Aachen

Fundamental questions regarding how current flows through a single molecule are closely related to the mechanical degrees of freedom, which distinguish single-molecule devices from artificially created nano-devices such as quantum dots. Recent experiment have revealed new, spectacular effects in the sequential tunneling regime due to this coupling of the electronic and mechanical degrees of freedom, e.g. Franck-Condon resonances and negative differential conductance. Vibration related resonances have also been observed in regimes where the sequential tunneling is suppressed by electron-electron interactions. Here the current is carried by correlated tunneling processes involving more than one electron. Such processes display more narrow resonances in the differential conductance, allowing more accurate spectroscopic information to be extracted, and may provide an important tool in the characterization of molecular junctions.
The goal of this research effort is to further develop a real-time transport theory for vibration-assisted, two-electron, tunneling processes (in-elastic co-tunneling). The real-time transport theory developed in our group allows a systematic perturbation expansion in the tunneling coupling in terms of diagrams on a Keldysh contour. At a given order of the perturbation expansion, all contributions proportional to this power of the tunneling coupling are accounted for. This includes renormalization and broadening of the many-particle states due to higher order tunneling events, which also modifies the sequential tunneling current. The electron-electron and electron-phonon interactions on the molecules are included in a non-perturbative way and the non-equilibrium condition induced by the bias voltage is taken into account in an exact manner. Extensions of the diagrammatic rules allow for coupling to a dissipative environment.
Development of this formalism will enable calculations under typical experimental conditions: strong electron-electron and electron-vibration interactions and a tunneling coupling that is moderate (rather than weak) compared to the temperature. This will enable the interpretation and direct analysis of experiments using models incorporating both experimentally known parameters and ab-initio input. Developing the formalism in a general way will enable us to go beyond the simplest model systems, in a controlled approximation. Taking non-diagonal elements of the vibrational density matrix into account will allow us to investigate cases where the tunneling coupling is comparable to the vibrational level-spacing, a regime where interference phenomena between tunneling processes through neighboring vibrational states become important.

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