Abstract
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.
Highlights
Electrical devices on the nanoscale have received substantial interest in the last decade [1]
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
This allows for detailed studies of phenomena such as inelastic charge transfer due to molecular vibrations [7,8,9], voltage driven conformational changes of the molecular backbone [10], Kondo physics [11], and Andreev reflections [6], to name but a few
Summary
Electrical devices on the nanoscale have received substantial interest in the last decade [1]. While the initial experiments were operated at room temperature, low temperatures down to the millikelvin range, the typical regime for devices in mesoscopic solid state physics, are accessible (see, e.g., [4,5,6]) This allows for detailed studies of phenomena such as inelastic charge transfer due to molecular vibrations [7,8,9], voltage driven conformational changes of the molecular backbone [10], Kondo physics [11], and Andreev reflections [6], to name but a few. Combining DFT with nonequilibrium Green’s functions (NEGF) allows us to capture essential properties of junctions with specific molecular structures and geometries [2,3,12,13] This provides insight into the electronic formations of contacted molecules and gives at least qualitatively correct results for currents and differential conductances. A detailed analysis of this scheme in comparison with numerically exact solutions is still elusive
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