A simple real-space scheme for periodic Dirac operators

We address in this work the question of discretization two-dimensional periodic Dirac Hamiltonians. Standard finite differences methods on rectangular grids are plagued with so-called Fermion doubling problem, which creates spurious unphysical modes. The classical way around difficulty used physics community is to Fourier space, inconvenience having compute decomposition coefficients Hamiltonian and related convolutions. propose a simple real-space method immune problem applicable all lattices. based spectral differentiation techniques. apply our numerical scheme study flat bands graphene subject magnetic fields twisted bilayer graphene.