Fluctuating-time and full counting statistics for quantum transport in a system with internal telegraphic noise

Abstract

Many molecular junctions display stochastic telegraphic switching between two distinct current values, which is an important source of fluctuations in nanoscale quantum transport. Using Markovian master equations, we investigate electronic fluctuations and identify regions of non-renewal behavior arising from telegraphic switching. Non-renewal behavior is characterized by the emergence of correlations between successive first-passage times of detection in one of the leads. Our method of including telegraphic switching is general for any source-molecule-drain setup, but we consider three specific cases. In the first, we model stochastic transitions between an Anderson impurity with and without an applied magnetic field B. The other two scenarios couple the electronic level to a single vibrational mode via the Holstein model. We then stochastically switch between two vibrational conformations, with different electron-phonon coupling λ and vibrational frequency ω, which corresponds to different molecular conformations. Finally, we model the molecule attaching and detaching from an electrode by switching between two different molecule-electrode coupling strengths γ. We find, for all three cases, that including the telegraph process in the master equation induces relatively strong positive correlations between successive first-passage times, with Pearson coefficient p ≈ 0.5. These correlations only appear, however, when there is telegraphic switching between two significantly different transport scenarios, and we show that it arises from the underlying physics of the model. We also find that, in order for correlations to appear, the switching rate ν must be much smaller than γ.

Revealing strong correlations in higher order transport statistics: a noncrossing approximation approach

“…23,62,63,66,67,[107][108][109][110][111] QME methods for evaluating FCS have been widely employed. 13,15,23,67,112 Their numerically exact generalization, the HEOM technique, 93,[113][114][115][116][117][118][119][120] has recently been generalized to FCS in the context of vibrationally coupled electronic transport. 26…”

Electronic statistics-on-demand: bunching, anti-bunching, positive and negative correlations in a molecular spin-valve

“…While a relatively recent addition to the analysis of charge fluctuations in open quantum systems [27], waiting time theory has developed rapidly in the last 10 years. Consequently, it has been used to investigate a wide variety of transport scenarios, such as tunneling through molecules with electron-electron [27][28][29][30] and electronphonon [31][32][33][34] interactions, telegraphic switching [35], double [36,37] and triple [38,39] quantum dots, superconducting junctions [40][41][42][43][44], coherent conductors [45][46][47], non-Markovian transport [48,49], periodically driven transport [50,51], and transport in the transient regime [52][53][54][55]. As opposed to the full counting statistics (FCS), which is the most prevalent method for analyzing charge fluctuations, the WTD provides information on transport at short timescales, particularly via correlations between successive waiting times [28,50,51,[56][57][58].…”

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

“…The structural flexibility of the organic framework makes the current-induced atomic motion one of the most critical processes to the performance of molecular electronic devices. Atomic nuclei feel the tug of the tunneling electrons, which can induce nonequilibrium excitations in the molecular vibrations 1-5 , atomic rearrangements and rotations 6,7 , as well as large-scale current-driven conformational changes such as chemical reactions 6,[8][9][10][11][12] , bond ruptures 13,14 , telegraphic switching between multiple geometries [15][16][17][18][19][20][21][22] , and structural instabilities [23][24][25][26][27][28][29][30] . Current-induced forces exerted by out-of-equilibrium electrons on nuclei result in heating within the system, consequently straining molecular bonds and decreasing the functionality and lifespan of the system.…”