Fragile phonon topology on the honeycomb lattice with time-reversal symmetry

Abstract

We use the methods of topological quantum chemistry to explore the topology of phonons on time-reversal symmetric crystals with the structure of the planar honeycomb (layer group $p6/mmm$). This approach is not tied to a particular model of atomic vibrations, but is applied to the most general dynamical matrix constrained only by the symmetries of the system. We show that four distinct fragile topological phonon phases are generically possible. Truncating the dynamical matrix to third nearest neighbors yields a model that realizes the different phonon topologies, characterized by the existence of phononic edge and corner modes and by Wilson loops with winding numbers one and two. Fitting the dynamical matrix to the DFT phonon bands shows that graphene is not very far from a topologically nontrivial phonon phase.

13 pages, 7 figures. Matches published version, new appendix on the relation between corner modes and the filling anomaly, added references

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• Dynamical Fragile Topology in Floquet Crystals
• Fractional corner charges in threefold-symmetric two-dimensional materials with fragile topology
• All hourglass bosonic excitations in the 1651 magnetic space groups and 528 magnetic layer groups
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