Geometric anisotropy induced higher-order topological insulators in nonsymmorphic photonic crystals

Abstract

To a significant extent, the rich physical properties of photonic crystals (PCs) are determined by the underlying geometry, in which the composed symmetry operator and their combinations contribute to their unique topological invariant to characterize the topological phases. In this work, we use geometric anisotropy in the 2D square lattice composed of four rectangle blocks. Due to the presence of glide symmetry, we show a variety of topological phase transitions in designed nonsymmorphic PCs and these transitions shall be understood in terms of the Zak phase and Chern number in synthetic space, as well as the pseudospin-2 concept, combinationally. Furthermore, Zak phase winding in the periodic synthetic parameter space yields high-order Chern number and double interface states. In terms of the extended Zak phase and pseudospin Hall effect, a higher-order topological insulator is constructed in the PC system. Based on the combination of different lattices, this represents a unique system that requires multiple topological concepts and indices for theoretical examination and understanding. The intriguing and abundant topological features are also sustained in the corresponding three-dimensional PC slab, which makes it a very interesting platform to control the flow of optical signals.