Fate of topological states in incommensurate generalized Aubry-André models

Abstract

We study one-dimensional optical lattices described by generalized Aubry-André models that include both commensurate and incommensurate modulations of the hopping amplitude. This brings together two interesting features of this class of systems: Anderson localization and the existence of topological edge states. We follow changes of the single-particle energy spectrum induced by variations of the system parameters, with focus on the survival of topological states in the localized regime.

5 pages, 5 figures

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• Introduction to topological superconductivity and Majorana fermions
• Localization in one-dimensional incommensurate lattices beyond the Aubry-André model
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Cited by in corpus (13)

• Observation of topological phase with critical localization in a quasi-periodic lattice
• Anderson localization transition in a robust $\mathcal{P}\mathcal{T}$-symmetric phase of a generalized Aubry-Andre model
• Breakdown of the correspondence between the real-complex and delocalization-localization transitions in non-Hermitian quasicrystals
• Dephasing-induced mobility edges in quasicrystals
• Non-Hermitian quasicrystal in dimerized lattices
• Localization and mobility edges in the off-diagonal quasiperiodic model with slowly varying potentials
• Emergent strength-dependent scale-free mobility edge in a non-reciprocal long-range Aubry-André-Harper model
• Phase diagram of a generalized off-diagonal Aubry-André model with p-wave pairing
• Mobility Edges in one-dimensional Models with quasi-periodic disorder
• Dephasing-assisted diffusive dynamics in superconducting quantum circuits
• Generalized Aubry-Andre-Harper Models in Optical Superlattices
• Arithmetic Tuning of Dynamical Critical Exponents in Quasiperiodic Localization Transitions
• Quantum localization in incommensurate tight-binding chains