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

Kosov, Daniel S.

doi:10.1063/1.4991038

Cited by 25 publications

(36 citation statements)

References 42 publications

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“…As we will observe, nonrenewal dynamics can emerge even under the Markovian assumption, indicating that correlations between successive waiting times arise from the internal dynamics of the quantum system. Although in mesoscopic electron transport, non-renewal statistics are a relatively new research premise [35,36,38,40,42,45,83], they have a long history in chemical physics, where they were used to describe single-molecule processes in spectroscopy [105][106][107]127] and kinetics [104,128].…”

Section: E Renewal Theorymentioning

confidence: 99%

“…Just as we can define probability distributions for time delays between two tunneling events, so can we also define distributions for multiple time delays between a series of tunneling events: the higher-order time distributions. Consider the second-order WTD [38]:…”

Section: E Renewal Theorymentioning

confidence: 99%

“…Alternatively, one could repeatedly measure the time τ it takes for the number of measured quantum jumps to reach n and construct a probability density distribution P (τ (n)), as we demonstrate in Fig.(1). The first quantity, n(t), is an example of a fixed-time statistic [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25], while τ (n) is an example of a fluctuating-time statistic [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42]. Considering the important role time-dependent fluctuations have, analysis of quantum fluctuations has therefore been focused on calculating either fixed-time and fluctuating-time statistics, and exploring the relationship between the two [42][43][44][45].…”

Section: Introductionmentioning

confidence: 99%

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Counting quantum jumps: A summary and comparison of fixed-time and fluctuating-time statistics in electron transport

Rudge

Kosov

2019

The Journal of Chemical Physics

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In quantum transport through nanoscale devices, fluctuations arise from various sources: the discreteness of charge carriers, the statistical non-equilibrium that is required for device operation, and unavoidable quantum uncertainty. As experimental techniques have improved over the last decade, measurements of these fluctuations have become available. They have been accompanied by a plethora of theoretical literature using many different fluctuation statistics to describe the quantum transport. In this paper, we overview three prominent fluctuation statistics: full counting, waiting time, and first-passage time statistics. We discuss their weaknesses and strengths, and explain connections between them in terms of renewal theory. In particular, we discuss how different information can be encoded in different statistics when the transport is non-renewal, and how this behavior manifests in the measured physical quantities of open quantum systems. All theoretical results are illustrated via a demonstrative transport scenario: a Markovian master equation for a molecular electronic junction with electron-phonon interactions. We demonstrate that to obtain non-renewal behavior, and thus to have temporal correlations between successive electron tunneling events, there must be a strong coupling between tunneling electrons and out-of-equilibrium quantized molecular vibrations.

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Section: E Renewal Theorymentioning

confidence: 99%

Section: E Renewal Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Counting quantum jumps: A summary and comparison of fixed-time and fluctuating-time statistics in electron transport

Rudge

Kosov

2019

The Journal of Chemical Physics

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“…The first is based on treating nuclear motion as harmonic vibrations around equilibrium and typically assuming linearized electronvibration coupling. Then either a master equation based method [37][38][39][40][41][42][43][44][45][46] or a NEGF method 1,2,5,47-51 is used to describe the system. All theoretical methods in the first category assume that the amplitudes of nuclear motion are small and nuclei vibrate harmonically about the zerocurrent equilibrium geometry.…”

Section: Introductionmentioning

confidence: 99%

Current-induced atomic motion, structural instabilities, and negative temperatures on molecule-electrode interfaces in electronic junctions

2020

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Molecule-electrode interfaces in molecular electronic junctions are prone to chemical reactions, structural changes, and localized heating effects caused by electric current. These can be exploited for device functionality or may be degrading processes that limit performance and device lifetime. We develop a nonequilibrium Green's function based transport theory in which the central region atoms and, more importantly, atoms on molecule-electrode interfaces are allowed to move. The separation of time-scales of slow nuclear motion and fast electronic dynamics enables the algebraic solution of the Kadanoff-Baym equations in the Wigner space. As a result, analytical expressions for dynamical corrections to the adiabatically computed Green's functions are produced. These dynamical corrections depend not only on the instantaneous molecular geometry but also on the nuclear velocities. To make the theoretical approach fully self-consistent, the same time-separation approach is used to develop expressions for the adiabatic, dissipative, and stochastic components of current-induced forces in terms of adiabatic Green's functions. Using these current induced forces, the equation of motion for the nuclear degrees of freedom is cast in the form of a Langevin equation. The theory is applied to model molecular electronic junctions. We observe that the interplay between the value of the spring constant for the molecule-electrode chemical bond and electronic coupling strength to the corresponding electrode is critical for the appearance of structural instabilities and, consequently, telegraphic switching in the electric current. The range of model parameters is identified to observe structurally stable molecular junctions as well as various different kinds of current-induced telegraphic switching. The interfacial structural instabilities are also quantified based on current noise calculations.

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“…When subsequent waiting times are correlated the renewal assumption is violated and these relationships no longer hold; the WTD contains information separate to the FCS. Interestingly, even in Markovian systems non-renewal behaviour can arise from telegraphic switching 14,15 , superconductivity 34 , quantum coherence 35 , and the presence of strong interactions 36,37 . WTD measurements are experimentally accessible via sophisticated real-time single-electron detection techniques [38][39][40][41][42] ; or alternatively the WTD may be reconstructed from low-order current correlation functions 43 .…”

Section: Introductionmentioning

confidence: 99%

Nonrenewal statistics in quantum transport from the perspective of first-passage and waiting time distributions

Rudge

Kosov

2019

Phys. Rev. B

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The waiting time distribution has, in recent years, proven to be a useful statistical tool for characterising transport in nanoscale quantum transport. In particular, as opposed to moments of the distribution of transferred charge, which have historically been calculated in the long-time limit, waiting times are able to detect non-renewal behaviour in mesoscopic systems. They have failed, however, to correctly incorporate backtunneling events. Recently, a method has been developed that can describe unidirectional and bidirectional transport on an equal footing: the distribution of firstpassage times. Rather than the time between successive electron tunnelings, the first-passage refers to the first time the number of extra electrons in the drain reaches +1. Here, we demonstrate the differences between first-passage time statistics and waiting time statistics in transport scenarios where the waiting time either cannot correctly reproduce the higher order current cumulants or cannot be calculated at all. To this end, we examine electron transport through a molecule coupled to two macroscopic metal electrodes. We model the molecule with strong electron-electron and electron-phonon interactions in three regimes: (i) sequential tunneling and cotunneling for a finite bias voltage through the Anderson model, (ii) sequential tunneling with no temperature gradient and a bias voltage through the Holstein model, and (iii) sequential tunneling at zero bias voltage and a temperature gradient through the Holstein model. We show that, for each transport scenario, backtunneling events play a significant role; consequently, the waiting time statistics do not correctly predict the renewal and non-renewal behaviour, whereas the first-passage time distribution does.

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

Cited by 25 publications

References 42 publications

Counting quantum jumps: A summary and comparison of fixed-time and fluctuating-time statistics in electron transport

Counting quantum jumps: A summary and comparison of fixed-time and fluctuating-time statistics in electron transport

Current-induced atomic motion, structural instabilities, and negative temperatures on molecule-electrode interfaces in electronic junctions

Nonrenewal statistics in quantum transport from the perspective of first-passage and waiting time distributions

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