Non-renewal statistics in quantum transport through the eyes of first-passage and waiting time distributions

Abstract

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 first-passage 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.

16 pages, 8 figures total

References in corpus (29)

• Franck-Condon blockade and giant Fano factors in transport through single molecules
• Theory of the Franck-Condon blockade regime
• Counting Statistics of Non-Markovian Quantum Stochastic Processes
• Tunneling through molecules and quantum dots: master-equation approaches
• Full counting statistics of super-Poissonian shot noise in multi-level quantum dots
• Simple bounds on fluctuations and uncertainty relations for first-passage times of counting observables
• Full Counting Statistics in Strongly Interacting Systems: Non-Markovian Effects
• Electron counting in quantum dots
• Co-tunneling current and shot noise in quantum dots
• Electron Waiting Times in Mesoscopic Conductors
• Super-poissonian noise, negative differential conductance, and relaxation effects in transport through molecules, quantum dots and nanotubes
• Wave-packet Formalism of Full Counting Statistics
• Full-counting statistics of charge and spin transport in the transient regime: A nonequilibrium Green's function approach
• Electron Waiting Times in Non-Markovian Quantum Transport
• Noise Correlations in a Coulomb Blockaded Quantum Dot
• Frequency-dependent current correlation functions from scattering theory
• Distributions of electron waiting times in quantum-coherent conductors
• Electronic waiting-time distribution of a quantum-dot spin valve
• Full counting statistics and shot noise of cotunneling in quantum dots and single-molecule transistors
• Electron waiting times in coherent conductors are correlated
• Full Counting Statistics for a Single-Electron Transistor, Non-equilibrium Effects at Intermediate Conductance
• Waiting time distributions of electron transfers through quantum dot Aharonov-Bohm interferometers
• First-passage times in renewal and nonrenewal systems
• Waiting time distribution for electron transport in a molecular junction with electron-vibration interaction
• Shot noise spectroscopy on a semiconductor quantum dot in the elastic and inelastic cotunneling regimes
• Nonrenewal statistics in transport through quantum dots
• Waiting time distribution revealing the internal spin dynamics in a double quantum dot
• Electron waiting times of a periodically driven single-electron turnstile
• Non-renewal statistics for electron transport in a molecular junction with electron-vibration interaction