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Topological Zero-Energy Modes in Gapless Commensurate Aubry-André-Harper Models

Topological Zero-Energy Modes in Gapless Commensurate Aubry-André-Harper Models

The Aubry-Andr\'e or Harper (AAH) model has been the subject of extensive theoretical research in the context of quantum localization. Recently, it was shown that one-dimensional quasicrystals described by the incommensurate AAH model has a nontrivial topology. In this Letter, we show that the commensurate off-diagonal AAH model is topologically …