Conditional statistics of electron transport in interacting nanoscale conductors

Sukhorukov, Eugene V.; Jordan, Andrew N.; Gustavsson, Simon; Leturcq, R.; Ihn, Thomas; Ensslin, Klaus

doi:10.1038/nphys564

Cited by 103 publications

(140 citation statements)

References 30 publications

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“…In our case, the current in the most interesting regime is proportional to t 2 x, where x is exponentially small in ⌬ / k B T. Since the tunneling amplitude t can, in principle, be made arbitrarily small, sequential tunneling becomes the dominant process. Recently, it was shown that noise spectroscopy deep inside the Coulomb-blockade regime is possible [23][24][25][26] and in agreement with the sequential-tunneling description.…”

Section: Model and Theoretical Methodsmentioning

confidence: 64%

Connection between noise and quantum correlations in a double quantum dot

2008

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We investigate the current and noise characteristics of a double quantum dot system. The strong correlations induced by the Coulomb interaction and the Pauli principle create entangled two-electron states and lead to signatures in the transport properties. We show that the interaction parameter , which measures the admixture of the double-occupancy contribution to the singlet state and thus the degree of entanglement, can be directly accessed through the Fano factor of super-Poissonian shot noise.

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Section: Model and Theoretical Methodsmentioning

confidence: 64%

Connection between noise and quantum correlations in a double quantum dot

2008

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“…2(a)]. For example, in quantum dot circuits in the Coulomb-blockade regime the dots act as the sites and the electrodes as the particle reservoirs [24,[32][33][34][35]. Driven by thermal fluctuations, particles make random transitions either between the system and the reservoirs or from one site to another.…”

Section: Modelmentioning

confidence: 99%

Unification and new extensions of the no-pumping theorems of stochastic pumps

Mandal¹

2014

EPL

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From molecular machines to quantum dots, a wide range of mesoscopic systems can be modeled by periodically driven Markov processes, or stochastic pumps. Currents in the stochastic pumps are delimited by an exact no-go condition called the no-pumping theorem (NPT). The letter presents a unified treatment of all the adaptations of NPT known so far, and further extends it to systems with many species of interacting particles.From the cargo transport to muscle contraction, a multitude of tasks inside our cells are performed by bimolecular complexes called the molecular motors. They have inspired researchers to design artificial molecular complexes capable of controlled directed motion, such as translation along an axle [1] or a DNA origami track [2] and rotation along a molecular ring [3], among others [4][5][6][7][8][9]. Control technique of the artificial molecular machines is fundamentally different from macroscopic machines, because the effects of inertia are negligible and friction and fluctuations play the dominant role in the molecular scale [4]. An effective strategy is to periodically modulate the environment of the system to drive the system out of equilibrium and utilize the relaxation dynamics to generate the desired directed motion. An example is provided by the experiments by Leigh et al. [3] where an average directed rotation was induced in the artificial molecular machine [3]catenane by periodic modulation of temperature, radiation and chemical concentrations.Periodic modulation of external parameters to pump a desired directed current in stochastic systems is called stochastic pumping. Success of this strategy is delimited by an exact condition, called the no-pumping theorem (NPT), which states that both the energy levels and the barriers of the system have to be varied to generate any directed current. Consider, for example, the [2]catenane complex composed of a small molecular ring interlocked with a larger molecular ring, as depicted schematically in Fig. 1(a). The numbers 1, 2, and 3 denote the metastable states of the smaller ring. In Ref.[3] the authors noted that the smaller ring could not be rotated along the larger ring unidirectionally just by the variation of the energies of the metastable states, even with the intuitively appealing strategy depicted in Fig. 1(b). Such unexpected observations have led to a number of recent studies on stochastic pumps [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29].The NPT has been adapted to a number of scenario depending on the nature of the system. Starting with the original formulation for closed single-particle systems [14], it has been generalized to both closed and open many-particle systems [24,29]. A curious feature of the open system NPT is that the particle reservoirs attached to the system need not be in equilibrium with each other at every moment; stochastic pumping will fail if just the time-averaged activities are the same (Eq. 20 below), along with other conditions of NPT [24]. This is in contrast to the us...

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“…In these systems, the low (kilo-hertz) tunneling rates allow for detection of individual electrons in real-time using a nearby quantum point contact whose conductance is sensitive to the charge occupations of the dots. 3,5,6 Although quantum effects are typically suppressed at the long time scales characterizing the charge transport, quantum dots provide a unique setting to experimentally test theoretical predictions for high-order statistics. Remarkably, time-dependent cumulants of the transferred charge beyond the 15th order have recently been measured in single-electron transport through a Coulomb blockade quantum dot [7][8][9] and a wealth of statistical data is now available.…”

Section: Introductionmentioning

confidence: 99%

Factorial cumulants reveal interactions in counting statistics

2011

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Full counting statistics concerns the stochastic transport of electrons in mesoscopic structures. Recently it has been shown that the charge transport statistics for noninteracting electrons in a two-terminal system is always generalized binomial: it can be decomposed into independent singleparticle events, and the zeros of the generating function are real and negative. Here we investigate how the zeros of the generating function move into the complex plane due to interactions and demonstrate that the positions of the zeros can be detected using high-order factorial cumulants. As an illustrative example we consider electron transport through a Coulomb blockade quantum dot for which we show that the interactions on the quantum dot are clearly visible in the high-order factorial cumulants. Our findings are important for understanding the influence of interactions on counting statistics, and the characterization in terms of zeros of the generating function provides us with a simple interpretation of recent experiments, where high-order statistics have been measured.

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Conditional statistics of electron transport in interacting nanoscale conductors

Cited by 103 publications

References 30 publications

Connection between noise and quantum correlations in a double quantum dot

Connection between noise and quantum correlations in a double quantum dot

Unification and new extensions of the no-pumping theorems of stochastic pumps

Factorial cumulants reveal interactions in counting statistics

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