Three-dimensional flat bands in nodal-line semimetals

Sparked by the discovery of unconventional superconductivity in twisted bilayer graphene, the study of flat-band physics has become a driving force in the search for new phases of matter. In a recent paper [1], we demonstrated how to lift this study into the third dimension by employing strain engineering in nodal-line semimetals. We further showed that the emerging three-dimensional (3D) flat bands lead to correlated phases, such as superconducting and magnetic phases. In this talk, we will discuss the mechanism leading to 3D flat bands with a focus on the celebrated HgTe materials class, which is well-known for realizing quantum-spin Hall insulators, 3D topological insulators, and Weyl semimetals. More specifically, we will present new results demonstrating that alloys of HgTe and structurally similar materials are another promising platform for the study of 3D flat bands and the associated correlated phases.

[1] A. Lau, T. Hyart, C. Autieri, A. Chen, and D. I. Pikulin, Phys. Rev. X 11, 031017 (2021)