Abstract
The discovery of quadrupole topology opens a new horizon in the study of topological phenomena. However, the existing experimental realizations of quadrupole topological insulators in symmorphic lattices with fluxes often break the protective mirror symmetry. Here, we present a theory for anomalous quadrupole topological insulators in nonsymmorphic crystals without flux using two-dimensional sonic crystals with and symmetry groups as concrete examples. We reveal that the anomalous quadrupole topology is protected by two orthogonal glide symmetries in square or rectangular lattices. The distinctive features of the anomalous quadrupole topological insulators include: (i) minimal four bands below the topological band gap, (ii) nondegenerate gapped Wannier bands and special Wannier sectors with gapped composite Wannier bands, and (iii) quantized Wannier band polarizations in these Wannier sectors. With no need for flux insertion, the protective glide symmetries are well preserved in the sonic-crystal realizations where higher-order topological transitions can be triggered by symmetry or geometry engineering.
- Received 18 January 2020
- Revised 16 June 2020
- Accepted 18 June 2020
DOI:https://doi.org/10.1103/PhysRevB.102.035105
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