Investigation of reconfigurable higher-order topological states in a valley photonic crystal

We demonstrate reconfigurable higher-order corner states in a honeycomb lattice simply via tuning the eigenfrequencies of the lattice sites. The underlying physical mechanism is revealed from a tight-binding model including both nearest-neighbor (NN) and next-nearest-neighbor (NNN) couplings, and is further investigated in a modulated valley photonic crystal (PC). Our results show that next-nearest-neighbor coupling, which is commonly lacking in previous studies of valley photonic crystals, plays an important role in creating abundant higher-order topological (HOT) states, and provides extra freedom to realize controllable higher-order topological phase transitions. The mechanism and method presented here can find applications in flexible functional photonic devices based on higher-order topology.