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We analyze the effects of a distortion of the nuclear potential of amolecular quantum dot (QD), as well as a shift of its equilibrium position, onnonequilibrium-vibration-assisted tunneling through the QD with a single level($\epsilon_d$) coupled to the vibrational mode. For this purpose, we derive anexplicit analytical expression for the Franck-Condon (FC) factor for adisplaced-distorted oscillator surface of the molecule and establish rateequations in the joint electron-phonon representation to examine thecurrent-voltage characteristics and zero-frequency shot noise, and skewness aswell. Our numerical analyses shows that the distortion has two importanteffects. The first one is that it breaks the symmetry between the excitationspectra of the charge states, leading to asymmetric tunneling properties withrespect to $\epsilon_d>0$ and $\epsilon_d<0$. Secondly, distortion (frequencychange of the oscillator) significantly changes the voltage-activated cascadedtransition mechanism, and consequently gives rise to a different nonequilibriumvibrational distribution from that of the case without distortion. Taken inconjunction with strongly modified FC factors due to distortion, this resultsin some new transport features: the appearance of strong NDC even for asingle-level QD with symmetric tunnel couplings; a giant Fano factor even for amolecule with an extremely weak electron-phonon interaction; and enhancedskewness that can have a large negative value under certain conditions.

Counting statistics of tunneling through a single molecule: effect of distortion and displacement of vibrational potential surface