Bulk-interface correspondence from quantum distance in flat band systems

Abstract The bulk-boundary correspondence is an integral feature of topological analysis and the existence boundary or interface modes offers direct insight into structure Bloch wave function. While only topology function has been considered relevant to modes, we demonstrate that another geometric quantity, so-called quantum distance, can also host a bulk-interface correspondence. We consider generic class two-dimensional flat band systems, where parabolic band-crossing with dispersive band. such bands are known be topologically trivial, show nonzero maximum distance between eigenstates around touching point guarantees at interfaces two domains different chemical potentials distance. Moreover, predict even explicit form dispersion relation decay length modes.