Dirac materials, unlike the Weyl materials, have not been found in experiments to support intrinsic topological surface states, as the surface arcs in existing systems are unstable against symmetrypreserving perturbations. Utilizing the proposed glide and time-reversal symmetries, we theoretically design and experimentally verify an acoustic crystal of two frequency-isolated three-dimensional Dirac points with Z2 monopole charges and four gapless helicoid surface states. arXiv:2001.06205v1 [cond-mat.mtrl-sci]

No abstract

No abstract

No abstract

The iterative Green's function, based on a cyclic reduction of block-tridiagonal matrices, has been the ideal algorithm, through tight-binding models, to compute the surface density of states of semi-infinite topological electronic materials. In this paper, we apply this method to photonic and acoustic crystals, using finite-element discretizations and a generalized eigenvalue formulation, to calculate the local density of states on a single surface of semi-infinite lattices. Three-dimensional examples of gapless helicoidal surface states in Weyl and Dirac crystals are shown and the computational cost, convergence, and accuracy are analyzed.