The topological criticality in disordered non-Hermitian system

Disorders have a rich influence on topological and localized properties. Here, we explore the effects of different type of disorders (intracell and intercell) on the non-Hermitian system. We first exhibit the phase diagram and find that the intracell disorder and intercell disorder can broaden and narrow the topological region, respectively. Moreover, the skin effect, which is unique in the non-Hermitian system, is broken by disorders. Furthermore, we propose the generalized localization length to settle the issue of how to determine the topological phase boundary explicitly in the disordered non-Hermitian system. Significantly, the rationality of this definition can be verified by similarity transformation, in which we prove that the topological invariant remains invariant. Finally, a byproduct of our definition is that one can analytically get the criticality of topology in the clean-limit non-Hermitian system.