Topological surface phonons in isostatic lattices with z=2d become finite-frequency surface phonons in superisostatic lattices with z>2d when next-nearest-neighbor springs or bending forces are added.
[1,2] with a change in the signs of the χ’s, so that the topological polarization is RT = − 1 2 ∑ µ Tµ signχµ, where Tµ are the primitive translation vectors
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Signatures of Topological Phonons in Superisostatic Lattices
Topological surface phonons in isostatic lattices with z=2d become finite-frequency surface phonons in superisostatic lattices with z>2d when next-nearest-neighbor springs or bending forces are added.