Electron counting of single-electron tunneling current

Fujisawa, Toshimasa; Hayashi, Toshiaki; Hirayama, Y.; Cheong, Hai Du; Jeong, Y. H.

doi:10.1063/1.1691491

Cited by 120 publications

(119 citation statements)

References 10 publications

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“…The counting statistics of electrons through quantum dots has recently raised considerable theoretical [38,39,40,41,42] as well as experimental [27,43,44,45,46] interest. The single electrons entering and exiting a quantum dot connected to two leads can be measured.…”

Section: Entropy Fluctuations For Electron Transport Trough a Sinmentioning

confidence: 99%

“…We can therefore calculate all the trajectory entropies' probability distributions using the GF method described in section IV C. We solve numerically the evolution equations for the g m (ıγ, t)'s associated with the different entropies for different values of γ with the initial condition g m (ıγ, 0) = p m (0). After calculating the G(ıγ, t)'s using (47), the probability distribution is obtained by a numerical inverse Fourier transform (44). In all calculations we used β = 5, ǫ = 1, a l = 0.2 and a r = 0.1.…”

Section: Entropy Fluctuations For Electron Transport Trough a Sinmentioning

confidence: 99%

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Entropy fluctuation theorems in driven open systems: Application to electron counting statistics

2007

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The total entropy production generated by the dynamics of an externally driven systems exchanging energy and matter with multiple reservoirs and described by a master equation is expressed as the sum of three contributions, each corresponding to a distinct mechanism for bringing the system out of equilibrium: nonequilibrium initial conditions, external driving, and breaking of detailed balance. We derive three integral fluctuation theorems (FTs) for these contributions and show that they lead to the following universal inequality: an arbitrary nonequilibrium transformation always produces a change in the total entropy production greater or equal than the one produced if the transformation is done very slowly (adiabatically). Previously derived fluctuation theorems can be recovered as special cases. We show how these FTs can be experimentally tested by performing the counting statistics of the electrons crossing a single level quantum dot coupled to two reservoirs with externally varying chemical potentials. The entropy probability distributions are simulated for driving protocols ranging from the adiabatic to the sudden switching limit.

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Section: Entropy Fluctuations For Electron Transport Trough a Sinmentioning

confidence: 99%

Section: Entropy Fluctuations For Electron Transport Trough a Sinmentioning

confidence: 99%

Entropy fluctuation theorems in driven open systems: Application to electron counting statistics

2007

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“…Fast and sensitive charge detectors and highly stable current bias sources have made it possible to measure individual electrons crossing arrays of tunnel junctions 1 or quantum dots [2][3][4] ͑QDs͒. Directional forward and reverse counting through two quantum dots in a series has been reported.…”

Section: Introductionmentioning

confidence: 99%

“…The transitions between states can be measured by employing a quantum point contact. [2][3][4] As a reference point for the DQD junction, we also calculate the corresponding values for a QD with a single orbital where interferences are not possible.…”

Section: Introductionmentioning

confidence: 99%

Interference effects in the counting statistics of electron transfers through a double quantum dot

et al. 2008

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We investigate effects of quantum interferences and Coulomb interaction on the counting statistics of electrons crossing a double quantum dot in a parallel geometry by using a generating function technique based on a quantum master equation approach. The skewness and the average residence time of electrons in the dots are shown to be the quantities most sensitive to interferences and Coulomb coupling. The joint probabilities of consecutive electron transfer processes show characteristic temporal oscillations due to interference. The steady-state fluctuation theorem that predicts a universal relation between the number of forward and backward transfer events is shown to hold even in the presence of the Coulomb coupling and interference.

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“…Result (2) implies that the two currents may be either positively or negatively correlated, depending on the sign of Γ I. This effect has a simple physical interpretation: taking…”

mentioning

confidence: 99%

Conditional statistics of electron transport in interacting nanoscale conductors

Sukhorukov

Jordan

Gustavsson³

et al. 2007

Nature Phys

103

137

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There is an intimate connection between the acquisition of information and how this information changes the remaining uncertainty in the system. This trade-off between information and uncertainty plays a central role in the context of detection. Recent advances in the ability to make accurate, on-chip measurements of individual-electron current through a quantum dot 1-8 (QD) have been enabled by exploiting the sensitivity of a second current, passing through a nearby quantum point contact (QPC), to the fluctuating charge on the QD 4-8 . An important characteristic of QPC detectors is their minimal influence on the systems they probe. Here we show that even the operation of an effectively non-invasive QPC detector can statistically alter the system's behaviour. By observing a particular QPC current, the statistical distribution of the QD conditional current undergoes a substantial change in comparison to that expected for unconditional shot noise 9 . These results are in almost perfect agreement with a theoretical model we develop to predict the joint current probability distribution and conditional transport statistics of interacting nanoscale systems.Noise is generally due to randomness, which can be classical or quantum in nature. Telegraph noise, where there is random switching between two stable states 10 , originates from such diverse phenomena as thermal activation of an unstable impurity 11-13 , non-equilibrium activation of a bistable system 14-17 , switching of magnetic domain orientation [18][19][20] , or a reversible chemical reaction in a biological ion channel 21 .In nanoscale conductors, where charge motion is quantum coherent over distances comparable to the system size, shot noise and telegraph noise have recently been shown to be two sides of the same coin 6,7,22,23 . A quantum dot (QD) is sufficiently small that it is effectively zero dimensional, and behaves as an artificial atom, holding a small number of electrons. Figure 1a shows the sample used in the experiment reported here. The QD is marked by the dotted circle 24 . An extra electron can tunnel into the QD from the source lead (S), stay in the QD for a random amount of time and then tunnel out into the drain lead (D) if the applied voltage bias exceeds the temperature. This singleelectron transport produces a fluctuating electrical current. In order to detect the statistical properties of this current, a sensitive electrometer with a bandwidth much higher than the tunnelling rates is required. The electrometer is a nearby quantum point contact (QPC) that is capacitively coupled to the QD via the Coulomb interaction. The voltage-biased QPC detector transports many electrons through a narrow constriction in the surrounding two-dimensional electron gas (represented with an arrow). The resistance of the QPC is susceptible to changes in the surrounding electrostatic environment, and can therefore be used to sense the presence (or absence) of an extra electron on the QD 4 . When the extra electron tunnels into or out of the QD, the current I ...

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Electron counting of single-electron tunneling current

Cited by 120 publications

References 10 publications

Entropy fluctuation theorems in driven open systems: Application to electron counting statistics

Entropy fluctuation theorems in driven open systems: Application to electron counting statistics

Interference effects in the counting statistics of electron transfers through a double quantum dot

Conditional statistics of electron transport in interacting nanoscale conductors

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