Microscale and Nanoscale Physics of Topological Metals

拓扑金属的特征是存在拓扑保护的带接触点，类似于基本Weyl费米子的色散或其各种推广。自2015年首次实验发现以来，拓扑金属构成了当代凝聚态研究的一个广阔领域。当拓扑金属的尺寸缩小到微米或纳米尺度时，如在薄膜中，探索较少的系统出现了。这些材料的主要特点不是Weyl费米子的存在（其拓扑保护是受限的），而是费米能级态在动量空间中同时连接而在实空间中断开的新特性。初步研究表明，这一特性在各种影响方面具有深远的影响。特别是，我们遇到了这些金属的新拓扑分类的可能性，非常规的扩散行为，对入射光的丰富，可控的响应，以及对近似超导性的特殊响应。这个艾米-诺特项目将以类似的多样化子项目的形式进行，其目标是提供对这些系统的广泛理论理解，并推动它们的实验实现。具体来说，我们将探索将这些金属的费米表面设计成不同拓扑形状的可能性，增强各种响应系数，包括电导率和光转换为电流，并实现密度波有序。这些系统的特殊性带来了计算上的挑战，这些挑战来自于打破对称的空间限制以及空间自由度和动量自由度的相互联系。我们将使用各种已知的分析和数值技术，我们将以新的方式结合和扩展这些系统。

Topological metals are characterized by the presence of topologically protected band-touching points that resemble the dispersion of elementary Weyl Fermions or various generalizations of it. Since the first experimental discovery in 2015, topological metals constitute a broad field of contemporary condensed-matter research. Much less explored systems are those which emerge when the size of the topological metal is reduced to the micro- or nanoscale, such as in thin films. The main peculiarity of these materials is not the presence of Weyl Fermions, which topological protection is confinement-broken, but the novel property of Fermi-level states being simultaneously connected in momentum space and disconnected in real space. Preliminary research indicates that this peculiarity has far reaching consequences in a variety of effects. In particular, we encounter the possibility for a novel topological classification of these metals, an unconventional diffusive behaviour, a rich, controllable response to incident light, and peculiar response to proximitized superconductivity. This Emmy-Noether project will act in form of similarly diversified subprojects, connected by the goal to provide a broad theoretical understanding of these systems and push their experimental realization. Specifically, we will explore possibilities to design the Fermi surface of these metals in topologically different shapes, enhance various response coefficients, including conductivity and the conversion of light into electric current, and enable density-wave order. The peculiarity of these systems brings computational challenges, arising from the symmetry-breaking spatial confinement and the interconnection of spatial and momentum degrees of freedom. We will use various known analytical and numerical techniques, which we will combine and extend in novel ways to be applicable for these systems.