Theoretical studies of quantum transport in molecular junctions using the density matrix hierarchy method: Nonadiabatic effects, anharmonic vibrations, and current fluctuations

分子结中的量子传输，即单个分子与金属或半导体电极的化学结合，是一个活跃的实验和理论研究领域。分子结提供了在纳米尺度上研究非平衡多体量子物理的基本方面的可能性，并且在分子电子学领域引起了极大的兴趣。从理论的角度来看，分子连接处输运的定量描述是一个重大的挑战。尽管近年来取得了进展，但缺乏非常精确的传输方法，可以应用于分子连接的现实模型。在本项目中，密度矩阵层次法将进一步发展并实现分子结的一般模型。这将提供一种方法，该方法可以显著扩展数值精确方法可寻址的系统范围，特别是具有非绝热耦合和实际势能面的模型。这对于低频振动很重要，在低频振动中，广泛使用的谐波近似通常是无效的，对于表现出大振幅运动的系统来说，这是必不可少的，例如，扭转运动或基于构象变化的分子开关。该方法将用于研究分子结中各种有趣的，但迄今为止大部分未被探索的机制和现象，包括由势能面圆锥交叉引起的非绝热效应，具有大振幅运动的系统中的非调和振动运动，例如低聚苯乙烯中的扭转运动，以及这些类型系统中的电流噪声。

Quantum transport in molecular junctions, that is a single molecule chemically bound to metal or semiconductor electrodes, is an active field of experimental and theoretical research. Molecular junctions provide the possibility to study fundamental aspects of nonequilibrium many-body quantum physics at the nanoscale and have been of great interest in the field of molecular electronics. From the point of view of theory, the quantitative description of transport in molecular junctions represents a significant challenge. Despite the progress in recent years, there is a lack of very accurate transport methods that can be applied to realistic models of molecular junctions. In this project, the density matrix hierarchy method shall be further developed and implemented for a general model of molecular junctions. This will provide a methodology which extends the range of systems addressable by numerically exact methods significantly, including in particular models with nonadiabatic coupling and realistic potential energy surfaces. This is of importance for low-frequency vibrations, where the widely used harmonic approximation is often invalid, and is indispensable for systems, which exhibit large amplitude motion such as, for example, torsional motion or molecular switches based on conformational changes. The methodology will be used to investigate a variety of interesting, but so far largely unexplored mechanisms and phenomena in molecular junctions including nonadiabatic effects induced by conical intersection of potential energy surfaces, anharmonic vibrational motion in systems with large amplitude motion, such as for example torsional motion in oligophenylenes, as well as current noise in these type of systems.