Two-dimensional photonic crystals made of six air holes on a core-shell
dielectric material has been proposed to study the newly emerged photonic
quantum spin Hall insulator. Specifically, radii modification of the air holes
and core-shell without breaking time-reversal (TR) symmetry are supported by
the C_6 point group symmetry upon a proposed scheme. It is shown that multiple
topological transitions from an ordinary insulator with zero spin Chern number
(Cs) to a topological insulator with a non-zero Cs can be achieved by modifying
the geometry of the photonic structure. Studying the two counter-propagating
helical edge modes which have the opposite group velocities are of individual
importance for various optical purposes like scattering-free waveguides
protected to various defects, disorders and strong light-matter interactions.
We show that topological edge states demonstrate slow light characteristics.
The findings emphasize the fact that exploring topological phase transition can
be applied as a unique approach for realizing light transport, robust energy
transportation and slow light in integrated photonic circuits and devices
