Bulk-Edge Correspondence (BEC) for Euler Class via Projected Green's Function Zeros

Projected Green’s function methods for detecting edge modes of periodic Hamiltonians date back to Harold Widom (1976). The connection to band topology is more recent, making explicit the connection between bulk wavefunctions and protected topological edge modes. These methods have even been adapted to construct spectral gaps in quasi-periodic systems and to restore BEC in non-Hermitian systems. This talk explores the application of these methods to Euler class topological invariants and the construction of an enhanced BEC from “iterated projection” of the projected Green’s function.