Electrical transport through a single-electron transistor strongly coupled to an oscillator

Doiron, C. B.; Belzig, Wolfgang; Bruder, Christoph

doi:10.1103/physrevb.74.205336

Cited by 41 publications

(51 citation statements)

References 42 publications

(56 reference statements)

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“…The asymmetry between adding and removing electrons is the root of the asymmetry in Coulomb blockade peaks [11]. We describe the coupled system using a master equation for the charge on the dot combined with a FokkerPlanck equation for the phase space distribution of the oscillator [23,24]. The central objects are the probabilities P 0 (x, u) and P 1 (x, u) to find the oscillator at position x and velocity u with 0 or 1 extra electrons on the dot; these satisfy master equations with x-dependent rates,…”

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Strong Electromechanical Coupling of an Atomic Force Microscope Cantilever to a Quantum Dot

et al. 2010

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We present theoretical and experimental results on the mechanical damping of an atomic force microscope cantilever strongly coupled to a self-assembled InAs quantum dot. When the cantilever oscillation amplitude is large, its motion dominates the charge dynamics of the dot which in turn leads to nonlinear, amplitude-dependent damping of the cantilever. We observe highly asymmetric lineshapes of Coulomb blockade peaks in the damping that reflect the degeneracy of energy levels on the dot, in excellent agreement with our strong coupling theory. Furthermore, we predict that excited state spectroscopy is possible by studying the damping versus oscillation amplitude, in analogy to varying the amplitude of an ac gate voltage.Coupling a nanomechanical object to quantum electronics provides a system that can be used to probe both the mechanics and the electronics with extreme sensitivity. It has been predicted that the electronics may be used to measure the quantum nature of the mechanical object [1], and the reverse-using the mechanics to measure the quantum nature of mesoscopic electronics-was recently demonstrated with superconducting qubits [2]. Electromechanical systems that have attracted considerable attention recently include quantum shuttles [3], and mechanics coupled to single electron transistors [4,5] or tunnel junctions [6,7]. In most systems studied both experimentally and theoretically, the interaction between the electronic and mechanical components is weak.In this paper we study strong coupling effects, both theoretically and experimentally, in an electromechanical system consisting of a quantum dot capacitively coupled to an atomic force microscope (AFM) cantilever. Electrons tunneling on and off the dot effectively damp the cantilever, and this damping exhibits Coulomb blockade peaks as a function of bias voltage similar to those well known in the dot conductance, even in the limit of weak coupling [8,9,10]. It has long been predicted that level degeneracy on the dot leads to lineshape asymmetry of Coulomb blockade peaks in the conductance [11]. Recently, we observed corresponding temperaturedependent peak shifts in the damping at weak coupling [10], but the lineshape asymmetry was far too small to be measured before now. However, by driving the cantilever to large oscillation amplitudes we enter a regime of strong coupling where its motion strongly modifies the tunneling rates on and off the dot, and leads to a dramatic enhancement of the lineshape asymmetry. This enhancement is much greater than expected from simply extrapolating the weak coupling theory; it is a non-adiabatic effect that stems from the similarity of timescales for dynamics of the cantilever and the dot. Furthermore, we predict that by measuring the damping versus bias voltage and oscillation amplitude, strong coupling provides a means to perform excited state spectroscopy on the dot. Note that very different strong coupling effects unrelated to degeneracy were recently reported for a driven carbon nanotube coupled to an embedded do...

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“…(4) and (5) following the approach of Ref. [24]. We assume the level structure of a cylindrically symmetric dot, which includes a 2-fold degenerate s shell and a 4-fold degenerate p shell [26].…”

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Strong Electromechanical Coupling of an Atomic Force Microscope Cantilever to a Quantum Dot

et al. 2010

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“…11 In this paper, we study the case of "slow" phonons at strong coupling, ⌫ӷ 0 for eV Ͼប 0 . 12,14,[25][26][27] The physical distinction between this case and the one of "fast" phonons, ⌫Ӷ 0 , can be understood in the following way: For fast phonons, every electron tunneling event occurs over many oscillator periods. Thus effectively electrons can only couple to ͑or "measure"͒ the energy ͑i.e., occupation number͒ of the oscillator.…”

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confidence: 99%

Self-consistent theory of molecular switching

2008

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We study the model of a molecular switch comprised of a molecule with a soft vibrational degree of freedom coupled to metallic leads. In the presence of strong electron-ion interaction, different charge states of the molecule correspond to substantially different ionic configurations, which can lead to very slow switching between energetically close configurations ͑Franck-Condon blockade͒. Application of transport voltage, however, can drive the molecule far out of thermal equilibrium and thus dramatically accelerate the switching. The tunneling electrons play the role of a heat bath with an effective temperature dependent on the applied transport voltage. Including the transport-induced "heating" self-consistently, we determine the stationary currentvoltage characteristics of the device and the switching dynamics for symmetric and asymmetric devices. We also study the effects of an extra dissipative environment and demonstrate that it can lead to enhanced nonlinearities in the transport properties of the device and dramatically suppress the switching dynamics.

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“…One of them is the interplay between quantum transport at the level of single electron and the mechanical motion of localized vibrations in various nanoscale devices. These include single-molecule junctions [3][4][5][6][7][8][9][10][11][12][13], suspended carbon nanotube quantum dots (CNT-QDs) [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31], and several types of nanoelectromechanical systems (NEMS) [32][33][34] as single-electron transistors [35][36][37][38][39], superconducting single-electron transistors [40][41][42][43][44][45], single-electron shuttles [46][47][48][49][50]…”

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confidence: 99%

Charge-vibration interaction effects in normal-superconductor quantum dots

2017

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We study the quantum transport and the nonequilibrium vibrational states of a quantum dot embedded between a normal-conducting and a superconducting lead with the charge on the quantum dot linearly coupled to a harmonic oscillator of frequency ω. To the leading order in the charge-vibration interaction, we calculate the current and the nonequilibrium phonon occupation by the Keldsyh Green's function technique. We analyze the inelastic, vibration-assisted tunneling processes in the regime ω < , with the superconducting energy gap , and for sharp resonant transmission through the dot. When the energy ε 0 of the dot's level is close to the Fermi energy μ, i.e., |ε 0 − μ| , inelastic vibration-assisted Andreev reflections dominate up to voltage eV . The inelastic quasiparticle tunneling becomes the leading process when the dot's level is close to the superconducting gap |ε 0 − μ| ∼ ± ω. In both cases, the inelastic tunneling processes appear as sharp and prominent peaks-not broadened by temperature-in the current-voltage characteristic and pave the way for inelastic spectroscopy of vibrational modes even at temperatures T ω. We also found that inelastic vibration-assisted Andreev reflections as well as quasiparticle tunneling induce a strong nonequilibrium state of the oscillator. In different ranges on the dot's level, we found that the current produces: (i) ground-state cooling of the oscillator with phonon occupation n 1, (ii) accumulation of energy in the oscillator with n 1, and (iii) a mechanical instability characterized by a negative damping coefficient. We show that ground-state cooling is achieved simultaneously for several modes of different frequencies. Finally, we discuss how the nonequilibrium vibrational state can be readily detected by the asymmetric behavior of the inelastic current peaks with respect to the gate voltage.

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Electrical transport through a single-electron transistor strongly coupled to an oscillator

Cited by 41 publications

References 42 publications

Strong Electromechanical Coupling of an Atomic Force Microscope Cantilever to a Quantum Dot

Strong Electromechanical Coupling of an Atomic Force Microscope Cantilever to a Quantum Dot

Self-consistent theory of molecular switching

Charge-vibration interaction effects in normal-superconductor quantum dots

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