Computing Edge States without Hard Truncation

We present a numerical method which accurately computes the discrete spectrum and associated bound states of semi-infinite Hamiltonians model electronic “edge” localized at boundaries one- two-dimensional crystalline materials. The problem is nontrivial since arbitrarily large finite “hard” (Dirichlet) truncations Hamiltonian in infinite bulk direction tend to produce spurious partially supported truncation. Our method, overcomes this difficulty, compute Green's function by imposing an appropriate boundary condition direction; then, spectral data recovered via Riesz projection. demonstrate our method's effectiveness studies edge graphene zig-zag presence defects modeled both tight-binding continuum PDE under difference discretization. may also be used study domain wall-type edges materials where directions; we for case distinct honeycomb structures joined along edge. expect useful designing novel devices based on precise wave-guiding states.