Band topology is characterized by properties invariant under smooth deformations, yet traditional topological invariants like symmetry indicators fail to distinguish all distinct topologies. In this talk, I will introduce stable real-space invariants (SRSIs) based on real-space orbital multiplicities. SRSIs remain invariant under smooth deformations, even with the inclusion of fictitious additional orbitals, capturing stable topological equivalence between phases. SRSIs not only assess the relative topology between stably inequivalent phases exhaustively, but also diagnose certain band topology that symmetry indicators cannot detect.
Next, I will show how SRSIs systematically classify photonic band structures. In the classification of 3D photonic bands, specific conditions from Maxwell’s equations necessitate the use of stable equivalence, which is captured by SRSIs. I will compare the band topology allowed in electronic and photonic systems using SRSIs. After highlighting the unique topological properties of photonic bands, I will discuss the broader implications of SRSIs for identifying topological phases beyond conventional band-theory approaches.
