(Co)irrep invisible topology of perfectly flat bands

In previous work [1], the authors developed a powerful method for constructing flat band models, explaining the flat bands in a myriad of crystalline materials [2]. Using Topological Quantum Chemistry, we derived sufficient criteria (in terms of momentum-space irreps) for diagnosing topologically nontrivial (i.e. topologically fragile or symmetry-protected semimetalic) flat bands. In this work, we show that some flat bands can still harbor nontrivial topology manifesting itself through gapless points or fragile topology, but otherwise not diagnosable through momentum-space irreps. We build a comprehensive, systematic, orbital-based understanding of this new “irrep-invisible” topology in all 1651 Shubnikov Space Groups, using the machinery of real space invariants. Supplementing our analysis with homotopy arguments we derive gapless criteria for irrep-invisible flat band semimetals. Finally, in some recently identified semimetallic flat band materials, we show that irrep-invisible fragile topology can arise upon gapping the flat bands with spin-orbit coupling.

[1] D. Calugaru et al. Nat. Phys. 18, 185–189 (2022)

[2] N. Regnault et al. Nature 603, 824–828 (2022)