Long transient dynamics in the Anderson-Holstein model out of equilibrium

Albrecht, K. F.; Martín‐Rodero, A.; Monreal, R.; Mühlbacher, Lothar; Yeyati, A. Levy

doi:10.1103/physrevb.87.085127

Cited by 48 publications

(99 citation statements)

References 47 publications

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“…Recent calculations, based on numerically exact methods such as diagrammatic quantum Monte Carlo (diagMC) [28], have indicated that for strong electron-phonon coupling there exists a regime in which different initial conditions lead to different transport properties at short times. In a subsequent work [29] it was demonstrated that this apparent bistability actually corresponds to a long transient dynamics leading to blockingdeblocking events associated with the polaron dynamics. More recent work [30] has confirmed the analysis and also explored the effect of including the dot-leads Coulomb repulsion.…”

Section: Introductionmentioning

confidence: 93%

Transient dynamics and waiting time distribution of molecular junctions in the polaronic regime

et al. 2015

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We develop a theoretical approach to study the transient dynamics and the time-dependent statistics for the Anderson-Holstein model in the regime of strong electron-phonon coupling. For this purpose we adapt a recently introduced diagrammatic approach to the time domain. The generating function for the time-dependent charge transfer probabilities is evaluated numerically by discretizing the Keldysh contour. The method allows us to analyze the system evolution to the steady state after a sudden connection of the dot to the leads, starting from different initial conditions. Simple analytical results are obtained in the regime of very short times. We study in particular the apparent bistable behavior occurring for strong electron-phonon coupling, small bias voltages, and a detuned dot level. The results obtained are in remarkably good agreement with numerically exact results obtained by quantum Monte Carlo methods. We analyze the waiting time distribution and charge transfer probabilities, showing that only a single electron transfer is responsible for the rich structure found in the short-time regime. A universal scaling (independent of the model parameters) is found for the relative amplitude of the higher order current cumulants in the short-time regime, starting from an initially empty dot. We finally analyze the convergence to the steady state of the differential conductance and of the differential Fano factor at the inelastic threshold, which exhibits a peculiar oscillatory behavior.

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Section: Introductionmentioning

confidence: 93%

Transient dynamics and waiting time distribution of molecular junctions in the polaronic regime

et al. 2015

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“…The celebrated Anderson-Holstein model, with a single electronic orbital coupled to a local phonon mode, exposes an intricate interplay between the electronic and nuclear degrees of freedom. The model has been extensively studied to reveal the behavior of the current and its fluctuations in different regimes of electron-phonon coupling, see for example [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] . An extension of the Anderson-Holstein model with a secondary phonon bath was examined in many studies, see e.g.…”

Section: Introductionmentioning

confidence: 99%

Full counting statistics of vibrationally assisted electronic conduction: Transport and fluctuations of thermoelectric efficiency

2015

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We study the statistical properties of charge and energy transport in electron conducting junctions with electron-phonon interactions, specifically, the thermoelectric efficiency and its fluctuations. The system comprises donor and acceptor electronic states, representing a two-site molecule or a double quantum dot system. Electron transfer between metals through the two molecular sites is coupled to a particular vibrational mode which is taken to be either harmonic or anharmonic-a truncated (twostate) spectrum. Considering these models we derive the cumulant generating function in steady state for charge and energy transfer, correct to second-order in the electron-phonon interaction, but exact to all orders in the metal-molecule coupling strength. This is achieved by using the nonequilibrium Green's function approach (harmonic mode) and a kinetic quantum master equation method (anharmonic mode). From the cumulant generating function we calculate the charge current and its noise and the large deviation function for the thermoelectric efficiency. We demonstrate that at large bias the charge current, differential conductance, and the current noise can identify energetic and structural properties of the junction. We further examine the operation of the junction as a thermoelectric engine and show that while the macroscopic thermoelectric efficiency is indifferent to the nature of the mode (harmonic or anharmonic), efficiency fluctuations do reflect this property.

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“…However, recent calculations of the nonequilibrium current based on time-dependent density functional theory seem to indicate that at long times the system reaches a dynamical state characterized by correlation-induced current oscillations 2 . Similarly, questions regarding hysteresis, bistability and the dependence of the steady-state current on the initial occupation have been raised in the context of inelastic transport through nanoscale quantum dots [3][4][5][6][7][8][9][10][11] . Addressing the issue of a unique steady-state is a challenging task for theory, as systems exhibiting bistability involve strong electron-electron or electron-phonon correlations.…”

Section: Introductionmentioning

confidence: 99%

Bistability in a nonequilibrium quantum system with electron-phonon interactions

et al. 2013

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The existence of more than one steady-state in a many-body quantum system driven out-ofequilibrium has been a matter of debate, both in the context of simple impurity models and in the case of inelastic tunneling channels. In this paper, we combine a reduced density matrix formalism with the multilayer multiconfiguration time-dependent Hartree method to address this problem. This allows us to obtain a converged numerical solution of the nonequilibrium dynamics. Considering a generic model for quantum transport through a quantum dot with electron-phonon interaction, we prove that a unique steady-state exists regardless of the initial electronic preparation of the quantum dot, consistent with the converged numerical results. However, a bistability can be observed for different initial phonon preparations. The effects of the phonon frequency and strength of the electron-phonon couplings on the nonequilibrium dynamics and on the emergence of bistability is discussed.

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Long transient dynamics in the Anderson-Holstein model out of equilibrium

Cited by 48 publications

References 47 publications

Transient dynamics and waiting time distribution of molecular junctions in the polaronic regime

Transient dynamics and waiting time distribution of molecular junctions in the polaronic regime

Full counting statistics of vibrationally assisted electronic conduction: Transport and fluctuations of thermoelectric efficiency

Bistability in a nonequilibrium quantum system with electron-phonon interactions

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