We present shot noise measurements on Au nanowires showing very pronounced vibration-mode features. In accordance to recent theoretical predictions the sign of the inelastic signal, i.e., the signal due to vibration excitations, depends on the transmission probability becoming negative below a certain transmission value. We argue that the negative contribution to noise arises from coherent two-electron processes mediated by electron-phonon scattering and the Pauli exclusion principle. These signals can provide unique information on the local phonon population and lattice temperature of the nanoscale system.

We recently became aware of a scaling error in the plots of Fig. 2 of our article. These plots were generated using an erroneous transmission factor T ͑͒ =1− ͱ 1−T͑͒ instead of the correct transmission factor T͑͒ =4⌫ L ⌫ R / ͓͑ − ⑀ d ͒ 2 + ⌫ 2 ͔. The rescaled plots exhibit the same qualitative aspect: the frontiers of the phase diagrams between the blue ͑negative sign of ⌬F n ͒ and the red ͑positive sign of ⌬F n ͒ regions are unchanged for ␣ → 1 while slightly shifted for decreasing ␣. The frontiers between the blue ͑red͒ regions and the white regions ͑physically not accessible͒ occurring for a critical transmission factor T =4␣ / ͑1+␣͒ 2 are also slightly modified by this scaling error.We thank Thomas Frederiksen for drawing our attention to this point.

We analyze the effect of electron-phonon coupling on the full counting statistics of a molecular junction beyond the lowest order perturbation theory. Our approach allows to take into account analytically the feedback between the non-equilibrium phonon and electronic distributions in the quantum regime. We show that for junctions with high transmission and relatively weak electron-phonon coupling this feedback gives rise to increasingly higher nonlinearities in the voltage dependence of the cumulants of the transmitted charges distribution. PACS numbers: 73.63.Rt, 72.70.+m Single molecule junctions and atomic chains suspended between metallic electrodes constitute a fascinating playground to explore the interplay between electronic and vibronic degrees of freedom, see e.g. Refs. [1][2][3][4][5]. The interest is now not only restricted to the understanding of the mean current-voltage characteristics but has been extended to noise properties 6 and, more generally, to the full counting statistics (FCS) of the transmitted charges. 7,8 An intense theoretical activity has been focussed on the analysis of the simplest model consisting in a resonant level coupled to a single phonon mode in the quantum coherent regime. 7-11 So far, however, several aspects of this problem remain to be clarified. A serious limitation of existing transport theories is that they do not take into account the influence of the non-equilibrium phonon fluctuations in the statistics of the transmitted electrons, namely the feedback of the phonon dynamics on the current-noise properties. 12 This limitation is associated with the breakdown of perturbation theory beyond the lowest order in electron-phonon (e-ph) coupling as reported in Refs. [13]. These works, which demonstrate the necessity of including non-perturbative effects in the analysis, are, however, limited to equilibrium properties of bulk materials or to individual molecules in the sequential tunneling regime.In this work we demonstrate, by a partial resummation of the perturbative expansion, the great impact of the feedback of the phonon dynamics on the quantum transport properties through nanoscale junctions with high transmission and relatively weak e-ph coupling. The actual signatures of phonon fluctuations result from the interplay of several energy scales, i.e. the tunneling rate Γ of electrons, the e-ph coupling λ, the phonon frequency ω 0 and the relaxation rate ∝ η of the local phonon mode due to the coupling with bulk phonons. Depending on the specific sample considered and the efficiency of the relaxation mechanism for the phonon population, one might obtain a regime characterized by a thermal phonon population when η ≫ λ 2 ω 0 /Γ 2 (equilibrated phonons) or a regime where a strong non-equilibrium population is generated when η ≪ λ 2 ω 0 /Γ 2 (unequilibrated phonons). We analyze the crossover between the two regimes and demonstrate that in the regime of unequilibrated phonons the electronic current-noise shows a strong nonlinear behavior as a function of the applied voltage ...