Simultaneous Manipulation of Line-Gap and Point-Gap Topologies in Non-Hermitian Lattices

Non-Hermiticity may significantly influence the topology of a photonic/electronic lattice, giving rise to point gaps, which have attracted much attention in recent years. While the influences of the point-gap topology on the bulk-boundary correspondence for the line gap have been widely studied, the topological lattice that simultaneously processes the line-gap and point-gap topological transitions has not been reported. Here, a strategy to simultaneously manipulate the line-gap and point-gap topologies in non-Hermitian lattices is proposed. By introducing the asymmetric intercell coupling, the line-gap topological transition process is demonstrated. By further considering the nonreciprocal coupling between the nearest neighboring unit cells, the point-gap and line-gap topological transitions can be simultaneously realized. Finally, the influence of the next nearest coupling on non-Hermitian line-gap and point-gap topologies is also discussed.

Automated summary

Non-Hermiticity can have a significant impact on the topology of photonic/electronic lattices, leading to the emergence of point gaps, which have been the subject of much research interest. While the influence of point-gap topology on the bulk-boundary correspondence for line gaps has been extensively studied, a topological lattice that simultaneously undergoes transitions in line-gap and point-gap topology has not been reported. Here, we propose a strategy to manipulate line-gap and point-gap topology simultaneously in non-Hermitian lattices. By introducing asymmetric intercell coupling, we demonstrate the process of line-gap topological transition. By further considering nonreciprocal coupling between nearest neighboring unit cells, simultaneous topological transitions in point-gap and line-gap can be achieved. Finally, we discuss the influence of next nearest coupling on non-Hermitian line-gap and point-gap topology.