Nonlinear effects of phonon fluctuations on transport through nanoscale junctions

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 nonequilibrium 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.

Figure 1

(a) Sketch of the model system. (b) Exchange (Fock) and (c) Hartree diagram, both appearing in the linked cluster expansion of the CGF at order ${\lambda }^2$. Bottom: fourth-order diagrams, i.e., (d) double bubble, (e) double exchange, and (f) rainbow diagram.

Figure 2

(Color online) (a) Mean number of phonons $⟨n⟩$ at $V=5{\omega }_0$ and ${\omega }_0/\Gamma =0.01$ as a function of $\eta$ shown for various values of $\lambda$. For comparison, the dotted curves show the results of the rate-equation approach, Eq. (10), for the same parameters. (b) Voltage dependence of $⟨n⟩$ for $\eta /\Gamma ={10}^{-6}$ and ${\omega }_0/\Gamma =0.01$.

Figure 3

(Color online) (a) Differential conductance and (b) derivative of the current noise with respect to voltage as function of voltage for various values of $\lambda$. Parameters used are ${\omega }_0/\Gamma =0.01$ and $\eta /\Gamma ={10}^{-6}$. The dotted (dashed) lines show the results of the rate equation approach for thermally equilibrated (unequilibrated) phonons for comparison, taken from Ref. 8.