Topological phase transition induced by modulating unit cells in photonic Lieb lattice

Abstract Topological photonics was embarked from realizing the first-order chiral state in gyromagnetic media, but its higher-order states were mostly studied in dielectric lattice instead. In this paper we theoretically unveil a hierarchy of topological phases under broken time-reversal symmetry, which include the first-order Chern, and the second-order dipole, quadrupole phases. Concretely, by relaxing a certain spatial symmetry of unit cell, versatile topological phases including both edge and corner states can be established to transit around, with bandgap closures marking the phase boundaries. 
Our results on gyromagnetic photonic crystals may broaden the scope of sublattice engineering design for topological phase manipulation, potentially enabling multifunctional disorder-resistant waveguides and integrated photonic circuits for information communication.