Topological edge states of continuous Hamiltonians

Abstract: This paper concerns the topological classification of continuous Hamiltonians that find applications in biased cold plasmas and photonics. Besides a magnetic bias, the Hamiltonians are parametrized by a plasma frequency and a fixed vertical wavenumber. Eight distinct phases of matter are identified as these parameters vary. When insulating gaps are shared by two such phases, asymmetric edge modes propagate along interfaces separating the two phases. Here we apply the notion of a bulk difference invariant (BDI) to this Hamiltonian, and show by numerical diagonalizations of interface Hamiltonians that after an appropriate regularization our BDI correctly predicts edge transport as described by a bulk edge correspondence. We also derive theoretical tools to compute the BDI and show the limitations of the bulk edge correspondence (BEC) when the phase transition is too singular.