The schematic picture of the two-terminal electron transport through a vibrating quantum dot weakly coupled (via narrow dielectric regions ) to the Luttinger liquid leads with the chemical potentials ( is the driving voltage). All the energies are counted from the Fermi energy, which chosen to be zero. Electrons tunnel from one lead to another by hopping on and off the dot level with the energy (elastic channel) and due to electron-vibron coupling they can emit or absorb vibrons (vibron-assisted tunneling). Inelastic channels are represented as side-levels with energies . The position of the dot levels with respect to the Fermi energy can be uniformly shifted by applying a voltage to the “gate” electrode.
Differential conductance (in units of ) as a function of driving voltage (in the units of ). Here we put ; ; and tune the level energy to the resonant position . Solid lines correspond to the case of noninteracting leads (a and b); dotted line , dash-dot line (a), dotted line , dash-dot line (b). Zero-bias (elastic) resonance peak is gradually suppressed with the increase of electron-electron correlations (decrease of Luttinger liquid parameter ) while the satellite peaks survive until (a). For the resonance-like behavior of differential conductance disappears, and the conductance scales as a power law of the bias voltage (b).
Differential conductance (in the units of ) as a function of level energy , counted from the Fermi energy. The bias voltage is sufficiently high to excite vibrons and to support electron transport through inelastic channels. All parameters are the same as for Fig. 2a and 2b, respectively.
Differential shot noise power (in the units of ) (a) and Fano factor as functions of the level energy in the nonlinear transport regime (b). The other parameters are the same as in Fig. 2b.
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