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

Abstract

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.

Adiabatic Green's function technique and transient behavior in time-dependent fermion-boson coupled models

“…Our calculation successfully demonstrates the gradual decay of sidebands after the pump has been decoupled from the electronic system. Existence of the dissipative environment is not a necessary condition to observe the decay in the adiabatic limit as opposed to the previous study [7,8,11,[16][17][18][19].…”

“…(3.6) and (3.19) in essentially exact forms. A number of works studied the nonequilibrium phenomena in the context of a quantum dot coupled to external leads [8][9][10][11][12][13][14][15][16]18,19]. The dot Hamiltonian is akin to the Lang-Firsov model we study in this paper.…”

“…A particular class of timedependent problems in which the Hamiltonian is periodic in time, H (t + T ) = H (t), can be treated in the Floquet framework [4,5]. Generalizations of the Floquet theory that include the coupling to the dissipative reservoir and the quench of the periodic drive have been studied extensively in the past [6][7][8][9][10][11][12][13][14][15][16][17][18][19].…”

Electron waiting times of a periodically driven single-electron turnstile

“…For coherent conductors, the distribution of electron waiting times can be obtained from a compact determinant formula containing the scattering matrix of the system [28,29]. Moreover, transient behaviors have been described using nonequilibrium Green's functions [30][31][32].…”

Charge-vibration interaction effects in normal-superconductor quantum dots

“…In its simple formulation, one assumes a linear coupling between the electron occupation on the dot and the oscillation's amplitude of one or more harmonic modes representing the local vibrations. This model has been theoretically investigated widely in literature with different variations, extensions, in different regimes and with various theoretical approaches , in particular using diagrammatic techniques [113][114][115][116][117][118][119][120], a resummation approach [121,122], and numerical and nonperturbative methods [123][124][125][126][127].…”