Universität Ulm, Institut für Theoretische Physik, Albert-Einstein-Allee 11, 89069 Ulm, Germany.
Beilstein J Nanotechnol. 2011;2:416-26. doi: 10.3762/bjnano.2.47. Epub 2011 Aug 3.
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.
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.
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.
随着纳米尺度电路制造技术的发展，过去十年中分子电子学领域取得了令人瞩目的进展。然而，作为未来器件构建模块的分子接触的理论描述极具挑战性，因为它必须结合引线中费米液体的性质以及分子上的电荷和声子自由度。在特定设置的从头算方案之外，通用模型揭示了输运过程的特征。特别有吸引力的是基于在其他领域（如介观物理和分子内电子转移）成功使用的转移率的描述。然而，与数值精确解相比，对该方案的详细分析仍然难以捉摸。
我们表明，即使在严格预计会失效的参数空间区域（例如，在较低温度下），转移率的表述也提供了定量准确的描述。通常，分子内声子根据电压驱动的稳态分布，而这种稳态只能通过具有有效升高温度（加热）的热分布粗略捕获。扩展了电荷-声子复合物的主方程，以有效地包括约化密度矩阵的非对角元素的影响，即使对于更强的电子-声子耦合，也能提供非常准确的解。
速率描述和主方程提供了一种通用的模型，可以描述和理解通过分子结的电荷转移过程。与提供精确解作为基准的复杂数值模拟相比，这种方法在计算上要便宜几个数量级。可调节的参数（例如，从从头算计算中获得）允许处理各种实现。尽管它们的表述不如非平衡格林函数方法严格，但从概念上讲，它们更简单，更灵活，可以扩展，并且从实际角度来看，只要强量子相关性不会实质性地改变相关子单元的性质，它们就会提供准确的结果。
