Iterative summation of path integrals for nonequilibrium molecular quantum transport

Abstract

We formulate and apply a nonperturbative numerical approach to the nonequilibrium current I (V ) through a voltage-biased molecular conductor. We focus on a single electronic level coupled to an unequilibrated vibration mode (Anderson-Holstein model), which can be mapped to an effective three-state problem. Performing an iterative summation of real-time path integral (ISPI) expressions, we accurately reproduce known analytical results in three different limits. We then study the crossover regime between those limits and show that the Franck-Condon blockade persists in the quantum-coherent low-temperature limit, with a nonequilibrium smearing of step features in the I V curve.

Path-integral simulations with fermionic and bosonic reservoirs: Transport and dissipation in molecular electronic junctions

“…Second, while there are many studies where a perfectly harmonic mode is assumed, for example, see Refs. [20,21,24], to the best of our knowledge our work is the first to explore electron conduction in the limit of strong vibrational anharmonicity.…”

“…The iterative scheme, developed in Ref. [17], is based on the observation that in standard nonequilibrium situations and at finite temperatures bath correlations exponentially die [24,31], thus the IF can be truncated beyond a memory time τ c = N s δt, corresponding to the time where bath correlations sustain. Here N s is an integer, δt is the discretized time step, and the correlation time τ c is dictated by the bias and temperature.…”

“…The AH model has been simulated exactly with the secondary phonon bath, using a a real-time path-integral Monte Carlo approach [20], and by extending the multilayer multiconfiguration time-dependent Hartree method to include fermionic degrees of freedom [21]. More recently, the model has been simulated by adopting the iterative-summation of path-integral approach [22][23][24].…”

Nonclassical energy transfer in photosynthetic FMO complex

“…Additionally they are dependent on the chosen basis set. The exact methods such as hierarchical equations of motion or the path-integral techniques avoid these problems but require a lot of computational power [6,5]. Additionally, the density matrix describes the ensemble averaged system information.…”

Reconciling perturbative approaches in phonon-assisted transport junctions

“…Nuclear motion in conducting molecules and the surroundings governs effects such as local heating of the junction, which may lead to instabilities 11 , and incoherent tunnelling processes, responsible for the development of ohmic conduction 12 . These effects can be captured within simple models: The celebrated Anderson-Holstein model includes a single electronic site embedded between metals, further coupled to a single vibration, or a harmonic bath [13][14][15][16][17][18][19][20][21][22][23][24][25][26] . A different class of problems, relevant as well to photovoltaic devices 27 , concerns donor-acceptor type molecular systems, with two electronic sites coupled to molecular vibrations 11,[28][29][30][31][32][33][34] .…”