Laboratoire de Physique Théorique
Toulouse - UMR 5152

In the field of molecular electronics, transport properties are strongly affected by the coupling to internal degrees of freedom. In particular, electron-phonon interaction strongly modulates I-V curves, both in semi-classical an quantal transport regimes [1].

In this work, we review current knowledge about transport proporties in molecular junctions coupled to a single local phonon mode. We summarize recent theoretical advances that investigate the full counting statistics (FCS) of transmitted charges, in the quantum regime of strong coupling to the lead and weak e-ph interaction [2,3,4]. We interpret the behavior of arbitrary higher order cumulant of the current operator in terms of a competition mechanism between elastic and inelastic processes and show how experimental consequences of this mechanism might be observed on noise properties, following the lines of Ref [5].

Finally, we extend the corresponding results valid in the perturbative quantum regime to higher orders in e-ph coupling strength, and show how to properly take into account the renormalized dynamics of the phonon mode, as well as its impact on the FCS[6]. Non perturbative results in e-ph interaction for the FCS are outlined in the quantum tunnel regime[6], that both reproduce known results of semi-classical calculations[1] and go beyond available knowledge in the litterature.

[1] A. Mitra, I. Aleiner and A. J. Millis,

Phys. Rev. B 69, 245302 (2004).

[2] R. Avriller and A. Levy Yeyati,

Phys. Rev. B(R), 80, 041309(2009).

[3] T.L. Schmidt and A. Komnik,

Phys. Rev. B(R), 80, 041307(2009).

[4] F. Haupt, T. Novotny and W. Belzig,

arXiv:0903.2268v1 (2009).

[5] O. Tal, M. Krieger, B. Leerink and J.M. van Ruitenbeek,

Phys. Rev. Lett. 100, 196804 (2008).

[6] R. Avriller, D. Urban and A. Levy Yeyati,

In preparation.