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arXiv · 2106.13444

Surface density-of-states on semi-infinite topological photonic and acoustic crystals

Yi-Xin Sha·Bo-Yuan Liu·Hao-Zhe Gao·Heng-Bin Cheng·Hai-Li Zhang·Ming-Yao Xia·Steven G. Johnson·Ling Lu
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Abstract

Iterative Green's function, based on 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. The three-dimensional (3D) examples of gapless helicoidal surface states in Weyl and Dirac crystals are shown and the computational cost, convergence and accuracy are analyzed.

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Yi-Xin Sha, Bo-Yuan Liu, Hao-Zhe Gao, Heng-Bin Cheng, Hai-Li Zhang, Ming-Yao Xia, Steven G. Johnson, Ling Lu. 2021-06-25. Surface density-of-states on semi-infinite topological photonic and acoustic crystals. https://doi.org/10.1103/physrevb.104.115131

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