Valley and Valley-like Split-ring Topological Photonic Crystal

Abstract: In the research of topological phases of matter, valley pseudospins have been introduced into photonic systems. Here, we construct a split-ring photonic crystal (SPC) in which the spilt rings are distributed according to the Kagome model. By rotating three split rings as a whole under the condition of ensuring the existence of C3v symmetry, we obtain a traditional two-band-inversion valley topology (2IVT) driven by opening twofold Dirac degeneracy point. When three split rings are rotated as a whole without ensuring the existence of C3v symmetry, a valley-like topology driven by opening twofold degeneracy point will exist. In particular, when three split rings are rotated separately, three-band-inversion valley-like topology (3IVT) will exist which is also driven by opening twofold degeneracy point. Valley topology and valley-like topology can be described by non-trivial Wannier band (WB) and bulk polarization (BP), and they both have the positive and negative refraction along the Zigzag domain-wall. Our research can be extended to other models, using controllable geometry to construct a variety of topological structures, so as to provide ideas for the research of new topological states.