Charge transfer through single molecule contacts: How reliable are rate descriptions?

Abstract

Summary Background: The trend for the fabrication of electrical circuits with nanoscale dimensions has led to impressive progress in the field of molecular electronics in the last decade. However, a theoretical description of molecular contacts as the building blocks of future devices is challenging, as it has to combine the properties of Fermi liquids in the leads with charge and phonon degrees of freedom on the molecule. Outside of ab initio schemes for specific set-ups, generic models reveal the characteristics of transport processes. Particularly appealing are descriptions based on transfer rates successfully used in other contexts such as mesoscopic physics and intramolecular electron transfer. However, a detailed analysis of this scheme in comparison with numerically exact solutions is still elusive. Results: We show that a formulation in terms of transfer rates provides a quantitatively accurate description even in domains of parameter space where strictly it is expected to fail, e.g., at lower temperatures. Typically, intramolecular phonons are distributed according to a voltage driven steady state that can only roughly be captured by a thermal distribution with an effective elevated temperature (heating). An extension of a master equation for the charge–phonon complex, to effectively include the impact of off-diagonal elements of the reduced density matrix, provides very accurate solutions even for stronger electron–phonon coupling. Conclusion: Rate descriptions and master equations offer a versatile model to describe and understand charge transfer processes through molecular junctions. Such methods are computationally orders of magnitude less expensive than elaborate numerical simulations that, however, provide exact solutions as benchmarks. Adjustable parameters obtained, e.g., from ab initio calculations allow for the treatment of various realizations. Even though not as rigorously formulated as, e.g., nonequilibrium Green’s function methods, they are conceptually simpler, more flexible for extensions, and from a practical point of view provide accurate results as long as strong quantum correlations do not modify the properties of the relevant subunits substantially.

Effect of broadening in the weak-coupling limit of vibrationally coupled electron transport through molecular junctions and the analogy to quantum dot circuit QED systems

“…This counterintuitive phenomenon has been reported by a number of groups [7,42,[81][82][83]. It is demonstrated in Fig.…”

“…In the following, we discuss vibrationally coupled electron transport, focusing on the counterintuitive phenomenon that, in the steady state regime, a larger level of vibrational excitation can be obtained for systems with a weaker electronic-vibrational coupling [7,42,[81][82][83]. To this end, we discuss the basics of the phenomenon in Sec.…”

“…This phenomenon has been reported in a number of theoretical studies [7,42,[81][82][83] and explained via the suppression of electronhole pair creation processes [82]. The latter study was based on Born-Markov theory and pointed out the connection between the limits of an infinite bias voltage and a vanishing electronic-vibrational coupling strength.…”

Single molecular shuttle-junction: Shot noise and decoherence

“…Quantum master equations, which stem from the Liouville-von Neumann equation [26,27] and the many-body Schrödinger equation [28], are widely applied to describe electromechanical vibrational junctions. In the junctions, charge-vibration (or electron-phonon) couplings play an important role, which can be treated in both incoherent [29][30][31][32][33] and coherent approaches [34,35]. In the incoherent approach, the off-diagonal couplings between electron tunneling and the vibrational states are not included.…”

A quasi-classical mapping approach to vibrationally coupled electron transport in molecular junctions

“…Examples of approximate methods are scattering theory, [36][37][38][39][40][41][42] nonequilibrium Greens function (NEGF) approaches, 17,[43][44][45][46][47][48][49][50][51][52][53][54] and master equation methods. 44,[55][56][57][58][59][60][61][62][63] In addition, a variety of numerically exact schemes have employed, including numerical pathintegral approaches, [64][65][66] the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method, 67, 68 the scattering state numerical renormalization group approach, 69 and a combination of reduced density matrix techniques and impurity solvers. 32,70 All these methods employ a quantum mechanical treatment of both the electronic and nuclear DoF.…”