Engineering Fragile Topology in Photonic Crystals: Topological Quantum Chemistry of Light

María Blanco de Paz, Maia G. Vergniory, Dario Bercioux, Aitzol García-Etxarri, Barry Bradlyn

Published 2019-03-06Version 1

In this Letter, we apply the recently developed theory of "Topological quantum chemistry" to the study of band structures in photonic crystals. We focus on a family of crystals formed by elliptical rods in a triangular lattice. We show that the symmetry of Bloch states in the Brillouin zone can be used to determine the locations of localized photonic Wannier functions, which can be moved between various positions in the unit cell by engineered band inversions. Finally we show that for certain parameter ranges there exist isolated topological bands which do not admit a well-localized Wannier description, representing the first physical instance of "fragile" topology.