Quantum transport in graphene - influence of disorder, electron-phonon interaction, electronic structure and functionalisation

该项目研究了界面、无序和电子相关性对石墨烯基结构的光学、光谱和输运性质的影响。我们理论研究的关键方面将是(i)无序石墨烯纳米带中的狄拉克电子波包时间演化/动力学，（ii）粒子散射或限制在门定义的石墨烯量子点中，使（Veselago）透镜或克莱因隧道开关成为可能，（iii）受外部时间相关电磁场影响的门控石墨烯中的电流共振，（iv）声子影响的非平衡输运通过接触石墨烯器件。(v)石墨烯双层中可能的激子形成和凝聚。为了捕捉电子结构、样品几何、无序、电子-电子/声子和自旋轨道相互作用的复杂相互作用，我们使用了散射理论和Keldysh Green函数形式化的分析方法，并将它们与基于切比雪夫展开和无换向子指数时间传播的条件良好的数值技术相结合。为了计算诸如局部态密度分布、粒子传输和电导、单粒子光谱函数或表征实际尺寸石墨烯器件的电子特性和电荷传输的光学响应等数量，这些算法被实现、优化并在当今的高性能超级计算机上运行。因此，最终目标是模拟和理解由DFG优先计划中的几个小组进行的传输和电子结构实验，并演示基于石墨烯的电子、等离子体和光子学的可能构建块的功能。

The project studies the influence of interfaces, disorder and electronic correlations on optical, spectral and transport properties of graphene based structures. Key aspects of our theoretical investigations will be (i) the Dirac electron wave packet time-evolution/dynamics in disordered graphene nanoribbons, (ii) particle scattering off or confinement in gate-defined graphene quantum dots that enable (Veselago) lensing or switching of Klein tunnelling, (iii) current resonances in gated graphene subjected to external time-dependent electromagnetic fields, (iv) phonon-affected non-equilibrium transport through contacted graphene devices, and (v) possible exciton formation and condensation in graphene bilayers. To capture the complex interplay of electronic structure, sample geometry, disorder, electron-electron/phonon and spin-orbit interactions, we use analytical approaches from scattering theory and the Keldysh Green function formalism and combine them with well-conditioned numerical techniques, based on Chebyshev expansion and commutator-free exponential time-propagation. In order to calculate quantities such as the distribution of the local density of states, particle transmission and conductance, the single-particle spectral function or the optical response that characterise the electronic properties and charge transport of real-sized graphene devices, the algorithms are implemented, optimised and run on present-day high-performance supercomputers. Thereby the ultimate objective is to model and understand transport and electronic structure experiments performed by several groups within the DFG priority programme and to demonstrate the functionality of possible building blocks for a graphene based electronics, plasmonics and photonics.