Anomalous non-Hermitian skin effect of chiral boundary states

The interplay between non-Hermitian systems and topological insulators has garnered significant attention in recent years. In the presence of gain and loss contrast, the topological chiral boundary states exhibit the non-Hermitian skin effect (NHSE). A widely accepted perspective is that the NHSE is intrinsically linked to the nontrivial winding of the point gap in the complex spectrum. In this study, we identify an anomalous NHSE in a Chern insulator subjected to a gain-loss domain wall. Specifically, we demonstrate that the chiral boundary states induced by the gain-loss domain wall transition into corner states---exhibiting the NHSE---under open boundary conditions. Intriguingly, this NHSE is not associated with a nontrivial point-gap topology. As evidence, we show that a projective twofold rotational symmetry ensures the absence of nontrivial spectral winding. We have also investigated the size-dependent decaying length of this anomalous NHSE and its hybridization with other typical NHSEs. The discovery of this anomalous NHSE sheds new insights into the underlying mechanism of NHSEs.