Gain-Loss-Induced Hybrid Skin-Topological Effect

Non-Hermitian topological effects are of crucial importance both in fundamental physics and applications. Here we discover the gain-loss-induced hybrid second-order skin-topological effect and the $\mathcal{P}\mathcal{T}$ phase transition in skin-topological modes. By studying a non-Hermitian Haldane model, we find that the topological edge modes are localized on a special type of corner, while the bulk modes remain extended. Such an effect originates from the interplay between gain, loss, and the chiral edge currents induced by the nonlocal flux, which can be characterized by considering the properties of the edge sites as a one-dimensional chain. We establish a relation between the skin-topological effect and the $\mathcal{P}\mathcal{T}$ symmetries belonging to different edges. Moreover, we discover the $\mathcal{P}\mathcal{T}$ phase transition with the emergence of exceptional points between pairs of skin-topological modes. Our results pave the way for the investigation of non-Hermitian topological physics and $\mathcal{P}\mathcal{T}$ phase transition in higher-dimensional systems.