Recent studies of disorder or non-Hermiticity induced topological insulators inject new ingredients for engineering topological matter. Here, we consider the effect of purely non-Hermitian disorders, a combination of these two ingredients, in a 1D coupled-cavity array with disordered gain and loss. Topological photonic states can be induced by increasing gain-loss disorder strength with topological invariants carried by localized states in the complex bulk spectra. The system showcases rich phase diagrams and distinct topological states from Hermitian disorders. The non-Hermitian critical behavior is characterized by the biorthogonal localization length of zero-energy edge modes, which diverges at the critical transition point and establishes the bulk-edge correspondence. Furthermore, we show that the bulk topology may be experimentally accessed by measuring the biorthogonal chiral displacement, which can be extracted from a proper Ramsey interferometer that works in both clean and disordered regions. The proposed coupled-cavity photonic setup relies on techniques that have been experimentally demonstrated and, thus, provides a feasible route toward exploring such non-Hermitian disorder driven topological insulators.
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