Coherent transfer of Cooper pairs by a movable grain

We study the charge transfer in a small grain oscillating between two leads. Coulomb blockade restricts the charge fluctuations in such a way that only zero or one additional electrons can sit on the grain. The system thus acts as a charge shuttle. We obtain the full counting statistics of charge transfer and discuss its behavior. For large oscillation amplitude the probability of transferringñ electrons per cycle is strongly peaked around one. The peak is asymmetric since its form is controlled by different parameters forñ > 1 andñ < 1. Under certain conditions the systems behaves as if the effective charge is 1/2 of the elementary one. Knowledge of the counting statistics gives a new insight on the mechanism of charge transfer.

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“…Current and noise are obtained by numerical differentiation, while the FCS is obtained by solving numerically Eq. (12).…”

Section: General Resultsmentioning

confidence: 99%

“…When the leads and the grain are superconducting the existence of phase coherent transport as been proposed. 12,13,14 Many papers studied theoretically the conditions for the realization of the instability or considered the dependence of the current on the external parameters. Only few papers investigated instead current fluctuations.…”

Section: Introductionmentioning

confidence: 99%

Full counting statistics of a charge shuttle

Pistolesi

2004

Phys. Rev. B

103

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“…The properties of the Cooper pair shuttle crucially depend on the decoherence mechanism which is also responsible in driving the system toward a steady state. The presence of dissipation modifies the current phase relation, but does not (in general) destroy the Josephson current 9,11 .…”

Section: Introductionmentioning

confidence: 99%

“…The essential condition to characterize the shuttling mechanism is that the grain must be in contact with a single electrode at any time. Following the original proposal of a normal shuttle Gorelik et al 9 introduce the Cooper pair shuttle where all the device (electrodes and central island) is in the superconducting state. Despite the fact that the central island is never connected to the two superconductors simultaneously, the Chalmers group has shown that the system is still capable to establish a global phase coherence and hence support a finite Josephson current 9,10 .…”

Section: Introductionmentioning

confidence: 99%

Transport properties of a periodically driven superconducting single-electron transistor

2007

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We discuss coherent transport of Cooper pairs through a Cooper pair shuttle. We analyze both the DC and AC Josephson effect in the two limiting cases where the charging energy EC is either much larger or much smaller than the Josephson coupling EJ . In the limit EJ ≪ EC we present the detailed behavior of the critical current as a function of the damping rates and the dynamical phases. The AC effect in this regime is very sensitive to all dynamical scales present in the problem. The effect of fluctuations of the external periodic driving is discussed as well. In the opposite regime the system can be mapped onto the quantum kicked rotator, a classically chaotic system. We investigate the transport properties also in this regime showing that the underlying classical chaotic dynamics emerges as an incoherent transfer of Cooper pairs through the shuttle. For an appropriate choice of the parameters the Cooper pair shuttle can exhibit the phenomenon of dynamical localization. We discuss in details the properties of the localized regime as a function of the phase difference between the superconducting electrodes and the decoherence due to gate voltage fluctuations. Finally we point how dynamical localization is reflected in the noise properties of the shuttle.

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“…Experimental work in relation to EM-SET structures range from the macroscopic [5] to the micrometer scale [6][7][8] and down to the nanometer scale [9]. Various aspects of electronic transport in such systems have been theoretically investigated in a series of articles [11][12][13][14][15][16][17][18][19][20].…”

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confidence: 99%

Energy pumping in a quantum nanoelectromechanical system

Nord

Gorelik

2005

Low Temperature Physics

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Fully quantized mechanical motion of a single-level quantum coupled to two voltage biased electronic leads is studied. It is found that there are two different regimes depending on the applied voltage. If the bias voltage is below a certain threshold (which depends on the energy of the vibrational quanta) the mechanical subsystem is characterized by a low level of excitation. Above a threshold the energy accumulated in the mechanical degree of freedom dramatically increases. The distribution function for the energy level population and the current through the system in this regime is calculated. During the past few years experimental methods of physics has seen an advancing capability to manufacture smaller and smaller structures and devices. This has lead to many new interesting investigations of nanoscale physics. Examples include, for instance, observation of the Kondo effect in single-atom junctions [1], manufacturing of single-molecular transistors [2], and so on. There has also been a great interest in the promising field of molecular electronics [3]. One of the main features of the conducting nanoscale composite systems is its susceptibility to significant mechanical deformations. This results from the fact that on the nanoscale level the mechanical forces controlling the structure of the system are of the same order of magnitude as the capacitive electrostatic forces governed by charge distributions. This circumstance is of the utmost importance in the so called electromechanical single-electron transistor (EM-SET), which has been in focus of recent research. The EM-SET is basically a double junction system where the additional (mechanical) degree of freedom, describing the relative position of the central island, significantly influences the electronic transport. Experimental work in relation to EM-SET structures range from the macroscopic [5] to the micrometer scale [6][7][8] and down to the nanometer scale [9]. Various aspects of electronic transport in such systems have been theoretically investigated in a series of articles [11][12][13][14][15][16][17][18][19][20].In Ref. 4 and Ref. 15 it was, among other things, shown that coupling the mechanical degree of freedom of an EM-SET to the nonequilibrium bath of electrons constituted by the biased leads, can lead to dynamical self excitations of the mechanical subsystem and as a result bring the EM-SET to the shuttle regime of charge transfer. This phenomena is usually referred to as a shuttle instability. In these papers the grain dynamics are treated classically and the key issue is that the charge of the grain, q t ( ), is correlated with its velocity, &( ) x t , in a way so that the time average, q t x ( ) & ¹ 0. Decreasing the size of the central island in the EM-SET structure to the nanoscale level results in the quantization of its mechanical motion. Charge transfer in this regime was studied theoretically in Ref. 10. However, the strong additional dissipation in the mechanical subsystem suggested in this paper keeps the mechanical subsystem in t...

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Coherent transfer of Cooper pairs by a movable grain

Cited by 61 publications

References 13 publications

Full counting statistics of a charge shuttle

Full counting statistics of a charge shuttle

Transport properties of a periodically driven superconducting single-electron transistor

Energy pumping in a quantum nanoelectromechanical system

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