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.

arXiv comment10 pages, 6 figures

References in corpus (70)

• Topological Insulators
• Topological insulators and superconductors
• Unpaired Majorana fermions in quantum wires
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Edge states and topological invariants of non-Hermitian systems
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Non-Hermitian Physics
• Localization transitions in non-Hermitian quantum mechanics
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Topological Origin of Non-Hermitian Skin Effects
• Anomalous edge state in a non-Hermitian lattice
• Non-Bloch Band Theory of Non-Hermitian Systems
• Topological energy transfer in an optomechanical system with exceptional points
• Non-Hermitian Boundary Modes
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Anomalous modulation of a zero bias peak in a hybrid nanowire-superconductor device
• Observation of Bulk Fermi Arc and Polarization Half Charge from Paired Exceptional Points
• Hybrid higher-order skin-topological modes in non-reciprocal systems
• Anti-Parity-Time Symmetric Optics via Flying Atoms
• Topological phase transition in non-Hermitian quasicrystals
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Geometrical meaning of winding number and its characterization of topological phases in one-dimensional chiral non-Hermitian systems
• Interplay of non-Hermitian skin effects and Anderson localization in non-reciprocal quasiperiodic lattices
• Multichannel Generalization of Kitaev's Majorana End States and a Practical Route to Realize Them in Thin Films
• Non-Hermitian Many-Body Localization
• Detecting a Majorana-Fermion Zero Mode Using a Quantum Dot
• Robust light transport in non-Hermitian photonic lattices
• Topological unification of time-reversal and particle-hole symmetries in non-Hermitian physics
• Majorana Fermions in superconducting 1D systems having periodic, quasiperiodic, and disordered potentials
• Majorana Fermions in superconducting wires: effects of long-range hopping, broken time-reversal symmetry and potential landscapes
• Topological Phases in Non-Hermitian Aubry-André-Harper Models
• Signature of Dispersing 1D Majorana Channels in an Iron-based Superconductor
• Localization in one-dimensional incommensurate lattices beyond the Aubry-André model
• Metal-insulator phase transition in a non-Hermitian Aubry-André-Harper Model
• Parity-time-symmetric topological superconductor
• Topological superconductor to Anderson localization transition in one-dimensional incommensurate lattices
• Exact ground states and topological order in interacting Kitaev/Majorana chains
• Skin effect and winding number in disordered non-Hermitian systems
• Non-Hermitian topology: a unifying framework for the Andreev versus Majorana states controversy
• Topological Phase Transition driven by Infinitesimal Instability: Majorana Fermions in Non-Hermitian Spintronics
• Exact mobility edges, $\mathcal{P}\mathcal{T}$-symmetry breaking and skin effect in one-dimensional non-Hermitian quasicrystals
• 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
• Non-equilibrium Josephson effect through helical edge states
• Relation between $\mathcal{P}\mathcal{T}$-symmetry breaking and topologically nontrivial phases in the SSH and Kitaev models
• Universality classes of non-Hermitian random matrices
• Many-body localization in a non-Hermitian quasi-periodic system
• Topological quantum wires with balanced gain and loss
• Anderson localization in the Non-Hermitian Aubry-André-Harper model with physical gain and loss
• Anomalous Josephson current via Majorana bound states in topological insulators
• Probing the existence and dynamics of Majorana fermion via transport through a quantum dot
• Non-Hermitian Skin Effects in Hermitian Correlated/Disordered Systems: Boundary-Sensitive/Insensitive Quantities and Pseudo Quantum Number
• Coulomb blockade of Majorana fermion induced transport
• PT Symmetric Aubry-Andre Model
• Boundary-dependent Self-dualities, Winding Numbers and Asymmetrical Localization in non-Hermitian Quasicrystals
• $\mathcal{P}\mathcal{T}$-breaking threshold in spatially asymmetric Aubry-Andre Harper models: hidden symmetry and topological states
• Simulating the exchange of Majorana zero modes with a photonic system
• Topological phases in Kitaev chain with imbalanced pairing
• Localization Transition in Incommensurate non-Hermitian Systems
• Fate of Majorana zero modes, critical states and non-conventional real-complex transition in non-Hermitian quasiperiodic lattices
• Light Localization induced by Random Imaginary Permittivities
• PT-restoration via increased loss-gain in PT-symmetric Aubry-Andre model
• Current noise cross correlation mediated by Majorana bound states
• Spectral statistics, finite-size scaling and multifractal analysis of quasiperiodic chain with p-wave pairing
• Topological Anderson phase in quasi-periodic waveguide lattices
• Two scenarios for quantum multifractality breakdown
• Anomalous interference in Aharonov-Bohm rings with two Majorana bound states
• Vortices in a cylinder: Localization after depinning
• Photonic topological insulators induced by non-Hermitian disorders in a coupled-cavity array

Cited by in corpus (19)

• Localization transition, spectrum structure and winding numbers for one-dimensional non-Hermitian quasicrystals
• Dimerization induced mobility edges and multiple reentrant localization transitions in non-Hermitian quasicrystals
• 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