Phonon effects in molecular transistors: Quantum and classical treatment

We present a comprehensive theoretical treatment of the effect of electron-phonon interactions in molecular transistors, including both quantal and classical limits and we study both equilibrated and out of equilibrium phonons. We present detailed results for conductance, noise and phonon distribution in two regimes. One involves temperatures large as compared to the rate of electronic transitions on and off the dot; in this limit our approach yields classical rate equations, which are solved numerically for a wide range of parameters. The other regime is that of low temperatures and weak electron-phonon coupling where a perturbative approximation in the Keldysh formulation can be applied. The interplay between the phonon-induced renormalization of the density of states on the quantum dot and the phonon-induced renormalization of the dot-lead coupling is found to be important. Whether or not the phonons are able to equilibrate in a time rapid compared to the transit time of an electron through the dot is found to affect the conductance. Observable signatures of phonon equilibration are presented. We also discuss the nature of the low-T to high-T crossover.Comment: 20 pages, 19 figures. Minor changes, version accepted for publication in Phys. Rev.

Phonon-assisted Kondo Effect in a Single-Molecule Transistor out of Equilibrium

The joint effect of the electron-phonon interaction and Kondo effect on the nonequilibrium transport through the single molecule transistor is investigated by using the improved canonical transformation scheme and extended equation of motion approach. Two types of Kondo phonon-satellites with different asymmetric shapes are fully confirmed in the spectral function, and are related to the electron spin singlet or hole spin singlet, respectively. Moreover, when a moderate Zeeman splitting is caused by a local magnetic field, the Kondo satellites in the spin resolved spectral function are found disappeared on one side of the main peak, which is opposite for different spin component. All these peculiar signatures that manifest themselves in the nonlinear differential conductance, are explained with a clear physics picture.Comment: 12 pages, 6 figure