“…Valley edge modes have also been studied in plasmonic systems, e.g., in surface-wave photonic crystal on a single metal surface [184], designer surface plasmon crystal comprising metallic patterns deposited on a dielectric substrate [185], graphene plasmonic crystals [186][187][188][189], metal nanoparticles [190] and metal cylinders [191]. Valley edge modes have found a range of interesting applications, such as, lasing [192][193][194][195][196], fiber [197,198], reconfigurable devices [199][200][201], slow light [202][203][204][205], chiral coupling to quantum emitters [206][207][208], Mach-Zehnder interferometer [209], on-chip quantum information processing [210], long-range deformations [211], and logic gates [212]. Especially, for topological lasing based on valley edge modes, recently, an electrically pumped terahertz quantum cascade laser was experimentally demonstrated in a triangular lattice of quasi-hexagonal holes drilled through the active medium of a terahertz quantum cascade laser wafer [192] (see Fig.…”