Broken Symmetry and Coherence of Molecular Vibrations in Tunnel Transitions

Abstract

We examine the Breit-Wigner resonances that ensue from field effects in molecular single electron transistors (SETs). The adiabatic dynamics of a quantum dot elastically attached to electrodes are treated in the Born-Oppenheimer approach. The relation between thermal and shot noise induced by the source-drain voltage $V_{bias}$ is found when the SET operates in a regime tending to thermodynamic equilibrium far from resonance. The equilibration of electron-phonon subsystems produces broadening and doublet splitting of transparency resonances helping to explain a negative differential resistance (NDR)of current versus voltage (I-V) curves. Mismatch between the electron and phonon temperatures brings out the bouncing-ball mode in the crossover regime close to the internal vibrations mode. The shuttle mechanism occurs at a threshold $V_{bias}$ of the order of the Coulomb energy $U_c$. An accumulation of charge is followed by the Coulomb blockade and broken symmetry of a single or double well potential. The Landau bifurcation cures the shuttling instability and the resonance levels of the quantum dot become split because of molecular tunneling. We calculate the tunnel gaps of conductivity and propose a tunneling optical trap (TOT) for quantum dot isolation permitting coherent molecular tunneling by virtue of Josephson oscillations in a charged Bose gas. We discuss experimental conditions when the above theory can be tested.