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Abstract
The Anderson-Holstein model with Caldeira-Leggett coupling with environment is considered to describe the damping effect in a single molecular transistor (SMT) which comprises a molecular quantum dot (with electron-phonon interaction) mounted on a substrate (environment) and coupled to metallic electrodes. The electron-phonon interaction is first eliminated using the Lang-Firsov transformation and the spectral density function, charge current and differential conductance are then calculated using the non-equilibrium Keldysh Green function technique. The effects of damping rate, and electron-electron and electron-phonon interactions on the transport properties of SMT are studied at zero temperature.
Highlights
The Anderson-Holstein model with Caldeira-Leggett coupling with environment is considered to describe the damping effect in a single molecular transistor (SMT) which comprises a molecular quantum dot mounted on a substrate and coupled to metallic electrodes
They have suggested that the effect of dissipative surroundings around the molecule is to provide an additional broadening of the vibrational side bands
Other theoretical methods applied in this field include the Kinetic equation method[17,18], the rate equation approach[19], non-equilibrium Green’s function approaches[20,21,22] and numerical renormalization group method[23,24]
Summary
The substrate can cause a damping effect that can be described by a linear coupling term between the local phonon field of the molecule and a set of independent harmonic oscillators of the substrate bath. The first term Hl describes the Hamiltonian for the source (l = S) and the drain (l = D) and is given by. The second term Hm describes the Hamiltonian of the molecule and is given by. Where Gr(a)(ε) and G>(
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