Electron waiting times in coherent conductors are correlated

Dasenbrook, David; Hofer, Patrick P.; Flindt, Christian

doi:10.1103/physrevb.91.195420

Cited by 42 publications

(83 citation statements)

References 58 publications

(123 reference statements)

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“…[2][3][4][6][7][8][9][10][11]13,14 The question which we discuss in this paper is the following. When an electron transfers through a molecular junction, is there exists a correlation between waiting times for successive electron tunneling or they are statistically independent?…”

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confidence: 99%

Non-renewal statistics for electron transport in a molecular junction with electron-vibration interaction

Kosov

2017

The Journal of Chemical Physics

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Quantum transport of electrons through a molecule is a series of individual electron tunneling events separated by stochastic waiting time intervals. We study the emergence of temporal correlations between successive waiting times for the electron transport in a vibrating molecular junction. Using master equation approach, we compute joint probability distribution for waiting times of two successive tunneling events. We show that the probability distribution is completely reset after each tunneling event if molecular vibrations are thermally equilibrated. If we treat vibrational dynamics exactly without imposing the equilibration constraint, the statistics of electron tunneling events become non-renewal. Non-renewal statistics between two waiting times τ1 and τ2 means that the density matrix of the molecule is not fully renewed after time τ1 and the probability of observing waiting time τ2 for the second electron transfer depends on the previous electron waiting time τ1. The strong electron-vibration coupling is required for the emergence of the non-renewal statistics. We show that in Franck-Condon blockade regime the extremely rare tunneling events become positively correlated.

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confidence: 99%

Non-renewal statistics for electron transport in a molecular junction with electron-vibration interaction

Kosov

2017

The Journal of Chemical Physics

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“…The physical interpretation of this RTD (25) depends on the definition of L 0 , which is determined by the splitting of the total Liouvillian into monitored quantum jumps and the generator for background quantum dynamics. We will consider two cases -the electron and an electron tunnelling.…”

Section: S/d 21mentioning

confidence: 99%

“…The initial increase of the residence time at small temperature, so that electrons spend longer time in the nanoscale system before jumping out to the drain, is due to blocking of the available states in the drain electrode by spreading the thermal Fermi-Dirac distribution. As the temperature increases further, the electronic population of the nanoscale system starts to grow and the intermediate quantum (25), they are involved in the calculations of the normalisation: the RTD is normalised to unity if it is integrated over time from 0 to ∞ and is summed over all possible secondary quantum jumps. This is reflected in the monotonic decrease of average residence times at larger temperature.…”

Section: S/d 21mentioning

confidence: 99%

“…Recently, Goswami and Harbola used Brandes' approach and the Lindblad master equation to study stochastic quantum fluctuations in electron transport through a single electronic level [20]. The theory has so far mainly focused on distributions of waiting times between events detected by counting in either the source or collector only [19,[21][22][23][24][25][26].…”

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confidence: 99%

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Distribution of residence times as a marker to distinguish different pathways for quantum transport

Rudge

Kosov

2016

Phys. Rev. E

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Electron transport through a nanoscale system is an inherently stochastic quantum mechanical process. Electric current is a time series of electron tunnelling events separated by random intervals. Thermal and quantum noise are two sources of this randomness. In this paper, we used the quantum master equation to consider the following questions: (i) Given that an electron has tunnelled into the electronically unoccupied system from the source electrode at some particular time, how long is it until an electron tunnels out to the drain electrode to leave the system electronically unoccupied, where there were no intermediate tunnelling events ("the" tunnelling path)? (ii) Given that an electron has tunnelled into the unoccupied system from the source electrode at some particular time, how long is it until an electron tunnels out to the drain electrode to leave the system electronically unoccupied, where there were no intermediate tunnelling events ("an" tunnelling path)? (iii) What are the distributions of these times? We show that electron correlations suppress the difference between the and an electron tunnelling paths.Recently, there have been significant advances towards theoretical and experimental understanding of quantum electron transport through nanoscale systems. In the past, nanoelectronics research was largely focussed on the study of current-voltage characteristics, the main (macroscopic) observable from which information about microscopic details of electron transport is deduced. However, in recent years, the interest in current fluctuations has grown enormously due to the important physical information contained within them [1]. Additionally, current fluctuations started to play important role in single-molecule electronics determining intricate details of interface chemistry and electron-vibrational coupling [2][3][4][5][6][7][8][9][10] The waiting time distribution (WTD) is a natural physical quantity that describes the quantum transport of single electrons. WTDs for successive physical events have been extensively studied as tools to describe stochastic processes in a diverse range of fields, from applied mathematics and astrophysics to single-molecule chemistry [11][12][13][14][15]. WTDs were first applied to quantum processes in the 1980s in photon counting quantum optics experiments [16][17][18]. Recently, WTDs have been used to describe the statistics of single electron transport in nanoscale quantum systems. In 2008 Brandes published his seminal paper on WTDs in quantum transport [19]. His methodology succinctly calculates the distribution of waiting times for various pairs of electron tunnelling events in open quantum systems described by general Markovian master equations. Furthermore, the formalism highlights the connections between WTDs and other important statistical tools for describing stochastic quantum processes, such as shot noise, current fluctuations, and full counting statistics. Recently, Goswami and Harbola used Brandes' approach and the Lindblad master equation to study stochas...

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“…Dasenbrock et al [3] have shown the correlation of subsequent waiting times in the coherent transport through a quantum point contact described within the scattering matrix formalism. Here the study is extended to the case of quantum dots.…”

Section: Introductionmentioning

confidence: 99%