Topological Transitions with an Imaginary Aubry-Andre-Harper Potential

Abstract

We study one-dimensional lattices with imaginary-valued Aubry-Andre-Harper (AAH) potentials. Such lattices can host edge states with purely imaginary eigenenergies, which differ from the edge states of the Hermitian AAH model and are stabilized by a non-Hermitian particle-hole symmetry. The edge states arise when the period of the imaginary potential is a multiple of four lattice constants. They are topological in origin, and can manifest on domain walls between lattices with different modulation periods and phases, as predicted by a bulk polarization invariant. Interestingly, the edge states persist and remain localized even if the real line gap closes. These features can be used in laser arrays to select topological lasing modes under spatially extended pumping.

References in corpus (44)

• Unpaired Majorana fermions in quantum wires
• Quantized Electric Multipole Insulators
• Exceptional Topology of Non-Hermitian Systems
• Non-Hermitian Physics
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Symmetry and Topology in Non-Hermitian Physics
• Topological States and Adiabatic Pumping in Quasicrystals
• Anomalous edge state in a non-Hermitian lattice
• Lasing in topological edge states of a 1D lattice
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• The Quantum-Mechanical Position Operator in Extended Systems
• Topological Origin of Zero-Energy Edge States in Particle-Hole Symmetric Systems
• Complex Edge-State Phase Transitions in 1D Topological Laser Arrays
• Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
• Topological phase transition in non-Hermitian quasicrystals
• Topological Hybrid Silicon Microlasers
• Topologically protected midgap states in complex photonic lattices
• Observation of Topological Phase Transitions in Photonic Quasicrystals
• Interplay of non-Hermitian skin effects and Anderson localization in non-reciprocal quasiperiodic lattices
• Topological Zero-Energy Modes in Gapless Commensurate Aubry-André-Harper Models
• Photonic Topological Insulating Phase Induced Solely by Gain and Loss
• Higher-order topological corner states induced by gain and loss
• Topological Pumping over a Photonic Fibonacci Quasicrystal
• Topological invariance and global Berry phase in non-Hermitian systems
• Topological photonic crystal nanocavity laser
• Observation of a higher-order topological bound state in the continuum
• Bound states in the continuum of higher-order topological insulators
• Non-Hermitian mobility edges in one-dimensional quasicrystals with parity-time symmetry
• Phase transitions in a non-Hermitian Aubry-André-Harper model
• Tutorial: Computing topological invariants in two-dimensional photonic crystals
• Defect states emerging from a non-Hermitian flat band of photonic zero modes
• Many-body approach to non-Hermitian physics in fermionic systems
• PT Symmetric Aubry-Andre Model
• Symmetry-protected zero-mode laser with a tunable spatial profile
• $\mathcal{P}\mathcal{T}$-breaking threshold in spatially asymmetric Aubry-Andre Harper models: hidden symmetry and topological states
• Mode-Locked Topological Insulator Laser Utilizing Synthetic Dimensions
• Effects of Non-Hermiticity on Su-Schrieffer-Heeger Defect States
• Room temperature electrically pumped topological insulator lasers
• Coherent topological polariton laser
• Non-Hermitian Topological End-Mode Lasing in Polariton Systems
• Numerical calculation of the complex berry phase in non-Hermitian systems
• Polarization and entanglement spectrum in non-hermitian systems
• PT-symmetric optical superlattices
• Electric polarization and its quantization in one-dimensional non-Hermitian chains

Cited by in corpus (7)

• Non-Hermitian topology and criticality in photonic arrays with engineered losses
• Versatile Braiding of Non-Hermitian Topological Edge States
• Localization and mobility edges in non-Hermitian continuous quasiperiodic systems
• Convection-modulated topological edge mode and extended-localized criticality in thermal metamaterials
• Topological Anderson insulator phases in one dimensional quasi-periodic mechanical SSH chains
• Topology and criticality in non-Hermitian multimodal optical resonators through engineered losses
• Dissipation induced ergodic-nonergodic transitions in finite-height mosaic Wannier-Stark lattices