Delocalization of higher-order topological states in higher-dimensional non-Hermitian quasicrystals

The combination of the non-Hermitian skin effect (NHSE) and topological effects plays a crucial role in both fundamental and applied physics. Here, we show the interplay between the NHSE and topological effects in two- and three-dimensional quasicrystals. Unlike the delocalization of higher-order topological states (HOTSs) in crystals, we find that in non-Hermitian quasicrystals, HOTSs delocalize along the boundaries rather than in the bulk regions. Through effective analysis of the quasicrystal boundaries, we establish a physical connection between the unique lattice arrangement of quasicrystals and the delocalization of HOTSs. Our results offer some perspectives for investigating intriguing physical phenomena emerging from the combination of higher-dimensional quasicrystals, the NHSE, and topological effects, as well as for broadening their applications.