Vibrational Instability due to Coherent Tunneling of Electrons

EPL (Europhysics Letters) (Impact Factor: 2.1). 04/2001; 58(1). DOI: 10.1209/epl/i2002-00611-3
Source: arXiv


Effects of a coupling between the mechanical vibrations of a quantum dot placed between the two leads of a single electron transistor and coherent tunneling of electrons through a single level in the dot has been studied. We have found that for bias voltages exceeding a certain critical value a dynamical instability occurs and mechanical vibrations of the dot develop into a stable limit cycle. The current-voltage characteristics for such a transistor were calculated and they seem to be in a reasonably good agreement with recent experimental results for the single $C_{60}$-molecule transistor by Park et al.(Nature {\bf 407,} (2000) 57). Comment: 5 pages, 3 figures

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    • "This is in accordance with the general rule [18] that the voltage, the current, and the charge oscillations due to Josephson plasmons are less noisy and more entangled for strongly correlated system. The shuttle mechanism based on the tunnel Hamiltonian[7]-[14] is equivalent to the simplest possible Holstein-type polaron models 2 . These models ignore all complexity of the real molecular SETs: A detailed understanding of the charge screening, geometry of electrodes, hybridization with continuous and bound surface states, scattering off impurities is either absent or presented in a fragmented manner. "
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    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 Vbias 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 Vbias of the order of the Coulomb energy Uc. 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.
    12/2004: pages 635-676;
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    ABSTRACT: We study the tunneling conductance of nano-scale quantum ``shuttles'' in connection with a recent experiment (H. Park et al., Nature, 407, 57 (2000)) in which a vibrating C^60 molecule was apparently functioning as the island of a single electron transistor (SET). While our calculation starts from the same model of previous work (D. Boese and H. Schoeller, Europhys. Lett. 54, 66(2001)) we obtain quantitatively different dynamics. Calculated I-V curves exhibit most features present in experimental data with a physically reasonable parameter set, and point to a strong dependence of the oscillator's potential on the electrostatics of the island region. We propose that in a regime where the electric field due to the bias voltage itself affects island position, a "catastrophic" negative differential conductance (NDC) may be realized. This effect is directly attributable to the magnitude of overlap of final and initial quantum oscillator states, and as such represents experimental control over quantum transitions of the oscillator via the macroscopically controllable bias voltage. Comment: 6 pages, LaTex, 6 figures
    Physical Review B 05/2002; 67(24). DOI:10.1103/PhysRevB.67.245415 · 3.74 Impact Factor
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    ABSTRACT: We analyze the dynamics of a nanomechanical oscillator coupled to an electrical tunnel junction with an arbitrary voltage applied to the junction and arbitrary temperature of electrons in leads. We obtain the explicit expressions for the fluctuations of oscillator position, its damping/decoherence rate, and the current through the structure. It is shown that quantum heating of the oscillator results in nonlinearity of the current-voltage characteristics. The effects of mechanical vacuum fluctuations are also discussed.
    Physical review. B, Condensed matter 09/2002; 67(11). DOI:10.1103/PhysRevB.67.115312 · 3.66 Impact Factor
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