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A different type of topological phase dubbed topological inverse Anderson insulators is proposed, which is characterized by the disorder-induced extended bulk states from the flat-band localization and topological edge states. Based on the topological invariant, the behaviors of the localization length of the zero-energy modes, and quantum transport, we identify its existence in several all-band-flat models with the disordered potentials or hopping including the -flux Creutz ladder, the fully dimerized Su-Schrieffer-Heeger chain, and -flux diamond chain. Unlike the topological Anderson insulator, where disorder induces localization and exponential suppression of transport, the disorder-assisted quantum ballistic coherent transport can appear in the topological inverse Anderson insulator. In addition, our proposal and results could be realized by the current experimental techniques.
Zuo et al. (Wed,) studied this question.