Topological phases and Anderson localization in off-diagonal mosaic lattices

Abstract

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

9 pages including supplementary

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Cited by in corpus (10)

• Exact mobility edges for 1D quasiperiodic models
• From topological phase to Anderson localization in a two-dimensional quasiperiodic system
• Transport and localization properties of excitations in one-dimensional lattices with diagonal disordered mosaic modulations
• Resonances, mobility edges and gap-protected Anderson localization in generalized disordered mosaic lattices
• The odd-even effect of mosaic modulation period of quasi-periodic hopping on the Anderson localization in a one-dimensional lattice model
• Numerical Investigation of Localization in Two-Dimensional Quasiperiodic Mosaic Lattice
• Real spectra and phase transition of skin effect in nonreciprocal systems
• Coexistence of topological Anderson insulator and multifractal critical phase in a non-Hermitian quasicrystal
• Exact Mobility Edges in a Disorder-Free Dimerized Stark Lattice with Effective Unbounded Hopping
• Topological edge states and disorder robustness in one-dimensional off-diagonal mosaic lattices