Nonrenewal statistics in transport through quantum dots

Abstract

The distribution of waiting times between successive tunneling events is an already established method to characterize current fluctuations in mesoscopic systems. Here, I investigate mechanisms generating correlations between subsequent waiting times in two model systems, a pair of capacitively coupled quantum dots and a single-level dot attached to spin-polarized leads. Waiting time correlations are shown to give an insight into the internal dynamics of the system, for example they allow distinction between different mechanisms of the noise enhancement. Moreover, the presence of correlations breaks the validity of the renewal theory. This increases the number of independent cumulants of current fluctuation statistics, thus providing additional sources of information about the transport mechanism. I also propose a method for inferring the presence of waiting time correlations based on low-order current correlation functions. This method gives a way to extend the analysis of nonrenewal current fluctuations to the systems for which single-electron counting is not experimentally feasible. The experimental relevance of the findings is also discussed, for example reanalysis of previous results concerning transport in quantum dots is suggested.Comment: 16 pages, 13 figures. Accepted for publication in Phys. Rev.

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

“…28 Renewal theory assumes that successive waiting times between transport events are statistically independent equally distributed random variables. In this case the joint probability density of two successive waiting times w 2 (τ 2 , τ 1 ) can be factorised into a product of two single-time distributions w 1 (τ 2 )w 1 (τ 1 ), that means that the distribution is totally "renewed" after waiting time τ 1 .…”

Noise Enhancement due to Telegraphic Switching in a Two-Level Quantum Dot Coupled to Spin-Polarized Leads

“…Transitions pÒq Ø pÒÓq, associated with the tunneling of spin Ó electrons, cause the slow switching between these transport channels. Such a phenomenon, referred to as the telegraphic switching, is already known to generate both the super-Poissonian noise and the correlations between subsequent waiting times [4]. Additionally, the system may be trapped in the configuration pÓÓq which leads to the current blockade.…”

“…2a). Additionally, the randomness parameter is not equal to the Fano factor which indicates that the subsequent waiting times are correlated [4] (when the waiting times are uncorrelated, both parameters are always equal [9]). This is confirmed by the direct calculation of the cross-correlation of subsequent waiting times (Fig.…”

“…Later, it was shown that in single-level quantum dots with a finite value of the Coulomb coupling and energydependent tunneling rates the another mechanism of the noise enhancement can occur -the telegraphic switching between the fast and the slow current channels [4]. This phenomenon, in contrast to the dynamical channel blockade, can be associated with the presence of the correlation between subsequent waiting times separating the successive tunneling events.…”

“…One can also determine the cross-correlation (covariance) of two subsequent waiting times [4] x∆τ 1 ∆τ 2 y ¢ f fs f fz logpwps, zqq…”