Topological phase transitions and edge states in dielectric photonic crystals of triangular lattice

Recently, the emergence of topological edge state of matter raises new challenges in understanding the states of condensed matter and phase transitions beyond the the Ginzburg-Landau paradigm. The discovery of topological edge states of condensed matter also stimulate the development in other field, such as the realm of photonics, particularly in photonic crystals (PhCs). In this paper, we systematically evaluate accidental degeneracy and its topological nature in 2D core-shell dielectric photonic crystals of triangular lattice Accidental degeneracy is tuned by the inner and outer radii of the core-shell cylinder as well as its dielectric constant, which is different from deterministic degeneracy resulted from non-symmorphic (sublattice) symmetry. The topological phase transition is understood via a pseudo-time-reversal (PTR) stemmed from time-reversal (TR) symmetry and C
6v
lattice symmetry. We calculated the topological phase transition diagram for 2D core-shell dielectric photonic crystals as well as for its inverse structure. A k.p theory is developed to understand the connection with quantum spin Hall effect in condensed matter physics. Other accidental degeneracies such as Diraclike Cone and the quadratic degeneracy dispersions at the Γ point are also studied.