  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.

Optics