Anderson localization and topological phase transitions in non-Hermitian Aubry-André-Harper models with p-wave pairing

Abstract

We study non-Hermitian Aubry-André-Harper models with p-wave pairing, where the non-Hermiticity is introduced by on-site complex quasiperiodic potentials. By analysing the $\mathcal{P}\mathcal{T}$ symmetry breaking, winding numbers of energy spectra, localization and fractal dimensions of states, and fate of Majorana fermions, a complete phase diagram on Anderson localization and topological phase transitions is obtained. In particular, the non-Hermitian topological nature of Anderson localization phase transitions from extended to critical and then to localized phases is identified, using both analytical and numerical methods. In the critical phase the complex spectrum is topological nontrivial with a fractional winding number. In the localized phase the analytical localization length of states can apply to the Hermitian case, which is absent so far. Both the non-Hermiticity and disorder are detrimental to Majorana fermions.

10 pages, 6 figures

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Cited by in corpus (18)

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• Nonequilibrium dynamics of the localization-delocalization transition in the non-Hermitian Aubry-André model
• Entanglement phase transitions in non-Hermitian quasicrystals
• Non-Abelian generalization of non-Hermitian quasicrystal: PT-symmetry breaking, localization, entanglement and topological transitions
• Non-Hermitian butterfly spectra in a family of quasiperiodic lattices
• Topological delocalization transitions and mobility edges in the nonreciprocal Maryland model
• Engineering mobility in quasiperiodic lattices with exact mobility edges
• Topological triple phase transition in non-Hermitian quasicrystals with complex asymmetric hopping
• Hybrid scaling properties of localization transition in a non-Hermitian disorder Aubry-André model
• Exact complex mobility edges and flagellate spectra for non-Hermitian quasicrystals with exponential hoppings
• Universal scaling of Green's functions in disordered non-Hermitian systems
• Correlation-induced phase transitions and mobility edges in an interacting non-Hermitian quasicrystal
• Scale-free localization versus Anderson localization in unidirectional quasiperiodic lattices
• Localization and topological transitions in generalized non-Hermitian SSH models
• Exact mobility line and mobility ring in the complex energy plane of a flat band lattice with a non-Hermitian quasiperiodic potential
• Two-body interaction induced phase transitions and intermediate phases in nonreciprocal non-Hermitian quasicrystals
• Exact multiple complex mobility edges and quantum state engineering in coupled 1D quasicystals
• Coexistence of topological Anderson insulator and multifractal critical phase in a non-Hermitian quasicrystal