Topological insulators have an electronic structure that supports topologically protected surface states. Now it seems that crystal symmetry can likewise generate protected states in a new class of materials known as 'topological crystalline insulators'.
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Drew, H. The great topological expansion. Nature Phys 8, 779–780 (2012). https://doi.org/10.1038/nphys2473
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DOI: https://doi.org/10.1038/nphys2473