Abstract
Topological theory of multipole moments in condensed matter physics have recently been generalized to classical systems such as photonic and sonic crystals and several types of quadrupole topological photonic crystals (QTPCs) have already been investigated. However, preceding reports relevant to this issue dealt mainly with square lattice. In this work, we reveal that quadrupole topological phases can also be appeared in hexagonal photonic lattices with the C3v-crystalline symmetry. For this purpose, we extend the topological theory of bulk and Wannier-sector polarizations to the affine coordinate system for analyzing the topological characteristics of non-square lattice systems. The calculation results show that the hexagonal photonic crystals with C3-crystalline symmetry have the quadrupole moments quantized to 1/3, provided that all photonic bands below the gap in consideration are non-degenerate. The hexagonal QTPCs support topological edge and corner states, which are much stronger confined compared with the edge and corner modes originating from nontrivial bulk polarizations. The presented results have fundamental importance and pave the way towards the broader applications of higher-order photonic topological insulators.
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