Numerically exact, time-dependent treatment of vibrationally coupled electron transport in single-molecule junctions

Abstract

The multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) theory within second quantization representation of the Fock space, a novel numerically exact methodology to treat manybody quantum dynamics for systems containing identical particles, is applied to study the effect of vibrational motion on electron transport in a generic model for single-molecule junctions. The results demonstrate the importance of electronic-vibrational coupling for the transport characteristics. For situations where the energy of the bridge state is located close to the Fermi energy, the simulations show the time-dependent formation of a polaron state that results in a pronounced suppression of the current corresponding to the phenomenon of phonon blockade. We show that this phenomenon cannot be explained solely by the polaron shift of the energy but requires methods that incorporate the dynamical effect of the vibrations on the transport. The accurate results obtained with the ML-MCTDH in this parameter regime are compared to results of nonequilibrium Green's function theory.

Bistability in a nonequilibrium quantum system with electron-phonon interactions

“…This is a strong statement by itself, but it does not rule out bistability for different initial phonon preparations. To address this question, we combined the formalism described above for the RDM with the ML-MCTDH approach in second quantized representation (SQR) 23,28 . The ML-MCTDH-SQR method provides a tool to compute the currents in Eq.…”

“…The former are based on either a mean-field approximation or perturbative schemes, where the inclusion of higher order corrections is not always clear or systematic, and thus may lead to questionable results. Numerical brute-force approaches, such as time-dependent numerical renormalization-group techniques [12][13][14][15] , iterative [16][17][18] or stochastic [19][20][21][22] diagrammatic methods, and wave function based approaches 23 , have been very fruitful, but are limited in the range of parameters and timescales that can be studied.…”

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 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].…”

Symmetry breaking and restoration using the equation-of-motion technique for nonequilibrium quantum impurity models

“…In general, this many body out-of-equilibrium problem cannot be solved exactly but for a few simple cases [4][5][6][7] . Excluding recent developments based on brute-force approaches such as time-dependent numerical renormalization-group techniques [8][9][10] , iterative [11][12][13] or stochastic 14-18 diagrammatic techniques to real time path integral formulations, wave function based approaches 19 , or reduced dynamic approaches 20,21 , all suitable to relatively simple model systems, most theoretical treatments of quantum transport rely on approximations of some sort. One well studied approach is based on the nonequilibrium Green function (NEGF) formalism otherwise known as the Keldysh NEGF or the Schwinger-Keldysh formalism 22,23 , which is widely used to describe transport phenomena [24][25][26] .…”