Chern invariants of topological continua: A self-consistent nonlocal hydrodynamic model

Abstract

Topological systems are characterized by integer Chern invariants. In a continuous photonic system characterized by a local Drude model, the material response is ill-behaved at large wavenumbers, leading to noninteger Chern invariants and ambiguity in the existence of topological edge modes. This problem has been solved previously by introducing an ad hoc material model including a spatial cutoff material response, which leads to a finite Brillouin zone and integer invariants. In this work, we calculate Chern numbers in magnetized continuous plasma systems by considering the effect of nonlocality using a hydrodynamic (HD) Drude model. Then we argue that this model presents several advantages compared with the previous models, e.g., introducing physical response at large wavenumbers and integer Chern invariants with sum to zero without the need for an interpolated material response. Therefore the HD model forms a complete and self-consistent model, which resolves the Chern number issues in topological photonic continua.