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

TL;DR

This paper adapts the iterative Green's function method, traditionally used for electronic materials, to compute the surface density-of-states in semi-infinite topological photonic and acoustic crystals, demonstrating 3D examples with analysis.

Contribution

It introduces a finite-element based generalized eigenvalue approach for topological photonic and acoustic crystals, extending Green's function techniques beyond electronic systems.

Findings

Successfully computes surface states in 3D Weyl and Dirac photonic/acoustic crystals.

Analyzes computational cost, convergence, and accuracy of the method.

Demonstrates the method's effectiveness for semi-infinite topological lattices.

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.