Microscopic understanding of correlations in twisted van der Waals [hetero]structures

范德华异质结构，特别是最新一波扭曲石墨烯系统的宏伟前景之一，是由电子相互作用驱动的物质的新相。相应地，本研究项目被置于本SPP的研究区域C，目的是通过两种方法来增强我们对这些系统中相互作用效应的了解。一方面，我们想要探索超越双层和多层石墨烯范例的扭曲范德华异质结构的丰富动物园。这将在有效的低能或少带模型的定性水平上进行，这些模型是从密度泛函理论表征获得的，作为研究电子-电子关联的无偏方法的输入。另一方面，我们将我们的研究扩展到包括整个大的莫尔布里渊区，明确地在描述中保留了更大的高能自由度。这使得我们能够做出仅考虑费米能级附近的能带所不能找到的预测。第二种方法，同样是由合作理论小组在这个优先计划中获得的从头算输入，给了我们一个机会来开发定量控制的结果，这些结果不会潜在地受到复杂的强相互作用效应的阻碍，这些效应很容易在限制在少数最低频带的研究中发生。最后，我们还可以使用该方案来控制向下折叠到有效的少带模型，包括超出随机相位近似的屏蔽效应。这些研究的预期结果包括现有的和新的异质结构的相图，发现的相互作用基态的能量标度和相关的响应函数，以及关于这些系统中调谐可能性和材料趋势的信息。

One of the grand promises of van der Waals heterostructures, especially of the latest wave of twisted graphene systems, are novel phases of matter driven by electronic interactions. Correspondingly, the goal of this research project, placed in research area C of this SPP, is to enhance our knowledge about interaction effects in these systems in a two-fold approach. On the one hand, we want to explore the rich zoo of twisted van der Waals hetero-structures beyond the bi- and multi-layer graphene paradigm. This will be undertaken on the qualitative level of effective low-energy or few-band models obtained from density functional theory characterizations as input to unbiased methods for the study of electron-electron correlations. On the other hand, we extend our study to incorporate the entirety of the large moiré Brillouin zone, explicitly keeping a larger span of high-energy degrees of freedom in the description. This allows us to make predictions that cannot be found considering the bands near the Fermi level alone. This second approach, again fed with ab-initio input obtained by collaborating theory groups in this priority program, gives us a chance to develop quantitatively controlled results that are not potentially hampered by complicated strong-interaction effects that occur easily in studies restricted to the few lowest bands. Finally, we can also use this scheme for a controlled down-folding to effective few-band band models, including screening effects beyond the random phase approximation. The expected outcome of these studies includes phase diagrams for existing and novel hetero-structures, energy scales and relevant response functions for the interacting ground states found and information on tuning possibilities and material trends in these systems.