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We introduce a one-dimensional lattice model whose hopping amplitudes aremodulated for equally spaced sites. Such mosaic lattice exhibits manyinteresting topological and localization phenomena that do not exist in theregular off-diagonal lattices. When the mosaic modulation is commensurate withthe underlying lattice, topologically nontrivial phases with zero- andnonzero-energy edge modes are observed as we tune the modulation, where thenontrivial regimes are characterized by quantized Berry phases. If the mosaiclattice becomes incommensurate, Anderson localization will be induced purely bythe quasiperiodic off-diagonal modulations. The localized eigenstate is foundto be centered on two neighboring sites connected by the quasiperiodic hoppingterms. Furthermore, both the commensurate and incommensurate off-diagonalmosaic lattices can host Chern insulators in their two-dimensionalgeneralizations. Our work provides a platform for exploring topological phasesand Anderson localization in low-dimensional systems.

Topological phases and Anderson localization in off-diagonal mosaic lattices