Exact Mobility edges and topological Anderson insulating phase in a slowly varying quasiperiodic model

Abstract

We uncover the relationship of topology and disorder in a one-dimensional Su-Schrieffer-Heeger chain subjected to a slowly varying quasi-periodic modulation. By numerically calculating the disorder-averaged winding number and analytically studying the localization length of the zero modes, we obtain the topological phase diagram, which implies that the topological Anderson insulator (TAI) can be induced by a slowly varying quasi-periodic modulation. Moreover, unlike the localization properties in the TAI phase caused by random disorder, mobility edges can enter into the TAI region identified by the fractal dimension, the inverse participation ratio, and the spatial distributions of the wave functions, the boundaries of which coincide with our analytical results.

arXiv comment9 pages, 8 figures

References in corpus (45)

• Topological Insulators
• Topological insulators and superconductors
• Weyl and Dirac Semimetals in Three Dimensional Solids
• Classification of topological quantum matter with symmetries
• Anderson localization of a non-interacting Bose-Einstein condensate
• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Colloquium: Topological Band Theory
• Topological Anderson Insulator
• Statistical Signatures of Photon Localization
• Non-Hermitian Topological Invariants in Real Space
• Theory of the topological Anderson insulator
• Topological phase transition in non-Hermitian quasicrystals
• Observation of the topological Anderson insulator in disordered atomic wires
• Photonic Topological Anderson Insulators
• Predicted mobility edges in one-dimensional incommensurate optical lattices: An exactly solvable model of Anderson localization
• Recent progress in many-body localization
• Topological Zero-Energy Modes in Gapless Commensurate Aubry-André-Harper Models
• Entanglement Spectrum of a Disordered Topological Chern Insulator
• Topological Criticality in the Chiral-Symmetric AIII Class at Strong Disorder
• One dimensional quasiperiodic mosaic lattice with exact mobility edges
• Topological Anderson Insulator in Three Dimensions
• Out-of-time-order correlations in many-body localized and thermal phases
• Metal-insulator phase transition in a non-Hermitian Aubry-André-Harper Model
• Topological superconductor to Anderson localization transition in one-dimensional incommensurate lattices
• Non-Hermitian mobility edges in one-dimensional quasicrystals with parity-time symmetry
• Non-Hermitian Topological Anderson Insulators
• Phase diagram of a non-Abelian Aubry-André-Harper model with $p$-wave superfluidity
• Anomalous mobility edges in one-dimensional quasiperiodic models
• The dependence of topological Anderson insulator on the type of disorder
• Topological Anderson Insulator in electric circuits
• Observation of topological phase with critical localization in a quasi-periodic lattice
• Localization and Mobility Gap in Topological Anderson Insulator
• Correlations due to localization in quantum eigenfunctions of disordered microwave cavities
• Topological Anderson insulators in two-dimensional non-Hermitian disordered systems
• Fate of zero modes in a finite Su-Schrieffer-Heeger Model with $\mathcal{P}\mathcal{T}$ Symmetry
• Topological Insulator in the Presence of Spatially Correlated Disorder
• Non-Hermitian Aubry-André model with Power-Law Hopping
• Disorder-induced Majorana zero modes in a dimerized Kitaev superconductor chain
• Topological Anderson phase in quasi-periodic waveguide lattices
• Novel mobility edges in the off-diagonal disordered tight-binding models
• Topological phase transition in the quasiperiodic disordered Su-Schriffer-Heeger chain
• Exact Mobility Edges and Topological Phase Transition in Two-Dimensional non-Hermitian Quasicrystals
• Topological Crystalline Phases in a Disordered Inversion-Symmetric Chain
• Anderson Topological Superconductor
• Mobility Edges in one-dimensional Models with quasi-periodic disorder

Cited by in corpus (11)

• Asymmetric transfer matrix analysis of Lyapunov exponents in one-dimensional non-reciprocal quasicrystals
• Su-Schrieffer-Heeger quasicrystal: Topology, localization, and mobility edge
• Emergent multi-loop nested point gap in a non-Hermitian quasiperiodic lattice
• Fibonacci-Modulation-Induced Multiple Topological Anderson Insulators
• Topological Anderson insulator phases in one dimensional quasi-periodic mechanical SSH chains
• Multiple reentrant topological windows induced by generalized Bernoulli disorder
• Disorder driven topological phase transitions in 1D mechanical quasicrystals
• Recent progress on disorder-induced topological phases
• Non-self-averaging topological Anderson insulator
• Topologically nontrivial multicritical points
• Coexistence of topological Anderson insulator and multifractal critical phase in a non-Hermitian quasicrystal