Topological-metal nanostructures

拓扑金属的特征是存在拓扑保护的带接触点，这类似于基本Weyl费米子的色散，因此在拓扑金属中色散可以采取各种修改形式。与这些Weyl费米子相关的手性异常的凝聚态物质实现，允许解决基本物理问题；与此同时，实验观察到的特殊输运现象使拓扑金属成为下一代技术应用中有前途的一类材料。在理论物理方面，我们遇到了新的挑战，这在很大程度上与手性异常或多或少的直接特征有关。手性异常在纳米和介观尺寸的拓扑金属研究中表现出一个有趣的方面。在这里，我们遇到了有关手性异常对其空间限制的高度非平凡响应的问题。许多以前用于理解凝聚态物质的理论模型是基于空间无限晶格的，并且只能捕获拓扑金属的一部分输运现象。这个项目的目的是将拓扑金属的理论模型扩展到空间受限系统。特别是，我将专注于开发特定的数值和分析工具来计算对电磁场的响应，考虑手性异常和其他相关的量子效应，以及空间限制对非平凡几何的影响和超导邻近的影响。这将允许设计和探索拓扑金属基纳米结构和异质结构（包括超导元素）的传输行为，以解释和预测新的传输现象。

Topological metals are characterized by the presence of topologically protected band-touching points, which resemble the dispersion of elementary Weyl Fermions, whereby in topological metals the dispersion can assume variously modified forms. The condensed-matter realization of the chiral anomaly, which is associated with these Weyl Fermions, allows to address fundamental physics problems; at the same time, peculiar transport phenomena that have been observed experimentally make topological metals a promising class of materials for the next generation of technological applications. On the theoretical-physics side we meet new challenges, in great part related to the more or less direct signatures of the chiral anomaly. A particular research field where the chiral anomaly shows an interesting facet is the research on topological metals of nano and mesoscopic size. Here we encounter questions concerned with the highly nontrivial response of the chiral anomaly to its spatial confinement. Many of the previously used theoretical models to understand condensed matter are based on spatially infinite lattices and can capture only a part of transport phenomena of topological metals. The aim of this project is to extend theoretical models of topological metals to spatially confined systems. In particular, I will focus on developing specific numerical and analytical tools to calculate the response to electromagnetic fields, accounting for the chiral anomaly and other relevant quantum effects, as well as the effect of spatial confinement to nontrivial geometries and the effect of superconducting proximity. This will allow to design and explore the transport behaviour of topological-metal based nanostructures and heterostructures including superconducting elements to explain and predict novel transport phenomena.