Even simple periodic mechanical lattices can exhibit exotic topologically protected modes. Incorporating defects into the mix makes things more interesting — revealing modes whose characteristics depend on properties of both the lattice and the defect.
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Witten, T. Of bagels and Burgers. Nature Phys 11, 95–96 (2015). https://doi.org/10.1038/nphys3232
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DOI: https://doi.org/10.1038/nphys3232