Microscale and Nanoscale Physics of Topological Metals

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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.