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。 我们的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）粒子散射或限制在栅极定义的石墨烯量子点中，（Veselago）透镜或Klein隧穿的切换，（iii）经受外部时间依赖性电磁场的门控石墨烯中的电流共振，（iv）通过接触的石墨烯器件的声子影响的非平衡输运，以及（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、样品几何形状、无序、电子-电子/声子和自旋-轨道相互作用的复杂相互作用，我们使用来自散射理论和Keldysh绿色函数形式主义的分析方法，并联合收割机它们与基于 切比雪夫展开与无扰子指数时间传播。 为了计算诸如局域态密度分布、粒子透射率和电导率、单粒子光谱函数或光学响应等物理量，这些物理量可以表征真实尺寸石墨烯器件的电子特性和电荷传输，这些算法可以在当今高性能超级计算机上实现、优化和运行。因此，最终目标是建立模型并理解DFG优先计划中几个小组进行的传输和电子结构实验，并展示基于石墨烯的电子学，等离子体和光子学的可能构建模块的功能。

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.