Skin-Anderson localization transitions in disordered hybrid-nonreciprocal systems

Abstract: Anderson (localization) transition is a universal wave phenomenon characterized by a disorder-induced quantum phase transition from extended to localized states, whereas the non-Hermitian skin effect is a generic feature of non-Hermitian systems that causes bulk states to localize at the boundaries. Here, we report an unexpected skin-Anderson localization transition arising from the interplay between these two phenomena in hybrid-nonreciprocal systems that exhibit both reciprocity and nonreciprocity in different spatial directions. In the weak-disorder regime, the states are boundary-extended, meaning they are extended in reciprocal spatial dimensions but localized at the boundaries in nonreciprocal dimensions due to the non-Hermitian skin effect. As disorder increases, these boundary-extended states transition to boundary-localized states at a critical disorder strength. Remarkably, the corresponding critical points exhibit universal characteristics akin to those of the Anderson transition in its Hermitian counterpart, including identical critical exponents within numerical errors. When disorder exceeds a higher critical threshold, a second transition occurs in which boundary-localized states become bulk-localized, thereby eliminating the non-Hermitian skin effect. Thus, the skin-Anderson localization transition establishes a new framework for controlling state localization by unifying the physics of Anderson transitions with non-Hermitian topology.