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See supplementary material at http://dx.doi.org/10.1063/1.4953364 for the derivation of mapping to the 2D topological mirror insulator; detailed parameters and relations between the tight-binding model for the purpose of reproducing the results; a standard definition of mirror Chern number in our system.[Supplementary Material]
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Abstract

Topological crystalline insulators are a class of materials with a bulk energy gap and edge or surface modes, which are protected by crystalline symmetry, at their boundaries. They have been realized in electronic systems: in particular, in SnTe. In this work, we propose a mechanism to realize photonic boundary states topologically protected by crystalline symmetry. We map this one-dimensional system to a two-dimensional lattice model with opposite magnetic fields, as well as opposite Chern numbers in its even and odd mirror parity subspaces, thus corresponding to a topological mirror insulator. Furthermore, we test the robustness of the boundary modes depending on their mirror parity by performing time dependent evolution simulations in a photonic setting with realistic experimental parameters.

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