Generalization of the one-step model of photo emission on the basis of the Keldysh formalism to describe time-dependent photo emission experiments

该理论项目旨在对固体系统中各种类型的随时间泵浦探针实验中观察到的光发射光谱进行从头算描述。准经典松弛模型与时间无关的单步光发射模型的结合将用于支持合作伙伴的实验工作，并为使用新的时间相关的单步光发射模型的计算提供参考结果。基于两次Keldysh形式主义的相应理论已经被申请人及其同事详细制定并部分实施。对于建立的与时间无关的单步模型的实现，电子结构将在密度泛函理论的框架内表示，并通过动态平均场理论（DMFT）进行扩展。为此，分别使用多重散射理论或Korringa-Kohn-Rostoker （KKR）形式主义，可以直接访问相应的延迟电子Green函数，并特别确保表面几何形状的适当表示。此外，在这种情况下，使用完全相对论的四组分狄拉克形式可以对所有自旋轨道诱导的二向色现象进行定量处理。在相对较弱的泵浦脉冲和低光子能量的价带光谱中，双光子光发射（2PPE）方法允许使用准摄动描述泵浦脉冲影响下初始状态的时间演化。相应的实现已经成功地应用于Ag（100）的2ppe光谱计算，将进一步优化并与实验伙伴等密切合作应用于拓扑绝缘体系统。对自旋极化情况的扩展将用于铁磁体Fe、Co和Ni的研究。为了解释强泵脉冲，将在以下开发中实现Keldysh形式主义的较小Green函数的Dyson方程的完全自一致解，以允许包含非线性效应。在进一步的发展中，动态相关性将在非平衡DMFT的基础上得到解释。为此，在前期工作中，根据二阶弱耦合方法推导出了相应的二次自能。将自洽性纳入已开发的依赖时间的一步模型将允许在相应的计算中考虑动态相关性，并将揭示这些在所得光谱中反映的程度。

The theory project aims for an ab-initio description of photo-emission spectra as observed in various types of time-dependent pump-probe experiments in solid state systems. The combination of a quasi-classical relaxation model and the time-independent one-step model of photo-emission will be used to support experimental work of collaboration partners and to supply reference results for calculations using a new time-dependent one-step model of photo-emission. The corresponding theory based on the two-time Keldysh formalism has been worked out in detail and already been partly implemented by the applicant and his coworkers. As for the established implementation of the time-independent one-step model the electronic structure will be represented in the framework of density functional theory and its extension via the dynamical mean field theory (DMFT). Using multiple scattering theory or the Korringa-Kohn-Rostoker (KKR) formalism, respectively, for this purpose gives direct access to the corresponding retarded electronic Green function and ensures in particular a proper representation of the surface geometry. Furthermore, using the fully relativistic four-component Dirac-formalism in that context allows for a quantitative treatment of all spin-orbit induced dichroic phenomena. The developed approach for two-photon photo-emission (2PPE) in valence band spectroscopy with relatively weak pump pulses and low photon energies permits to use a quasi-perturbative description of the time-evolution of the initial state under the influence of the pump pulse. The corresponding implementation, that has already been successfully applied for the calculation of 2PPE-spectra of Ag(100), will be further optimized and applied in close cooperation with experimental partners amongst others to Topological Insulator systems. The extension to the spin-polarized case will be used for investigations on the ferromagnets Fe, Co and Ni. To account strong pump pulses the full self-consistent solution of the Dyson equation for the lesser Green function of the Keldysh formalism will be implemented in a following development to allow inclusion of non-linear effects. Within a further development dynamical correlations will be accounted for on the basis of the non-equilibrium DMFT. For this purpose a corresponding two-time self-energy has been worked out within the preliminary work on the basis of second order weak coupling approach. The self-consistent inclusion into the developed time-dependent one-step model will allow to account for dynamical correlations within corresponding calculations and will reveal to which extent these are reflected in the resulting spectra.