Engineering non-Hermitian Second Order Topological Insulator in Quasicrystals

Abstract

Non-Hermitian topological phases have gained immense attention due to their potential to unlock novel features beyond Hermitian bounds. PT-symmetric (Parity Time-reversal symmetric) non-Hermitian models have been studied extensively over the past decade. In recent years, the topological properties of general non-Hermitian models, regardless of the balance between gains and losses, have also attracted vast attention. Here we propose a non-Hermitian second-order topological (SOT) insulator that hosts gapless corner states on a two-dimensional quasi-crystalline lattice (QL). We first construct a non-Hermitian extension of the Bernevig-Hughes-Zhang (BHZ) model on a QL generated by the Amman-Beenker (AB) tiling. This model has real spectra and supports helical edge states. Corner states emerge by adding a proper Wilson mass term that gaps out the edge states. We propose two variations of the mass term that result in fascinating characteristics. In the first variation, we obtain a purely real spectra for the second-order topological phase. In the latter, we get a complex spectra with corner states localized at only two corners. Our findings pave a path to engineering exotic SOT phases where corner states can be localized at designated corners.

References in corpus (79)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Topological Insulators with Inversion Symmetry
• Making Sense of Non-Hermitian Hamiltonians
• Classification of topological quantum matter with symmetries
• Nonreciprocal light transmission in parity-time-symmetric whispering-gallery microcavities
• Topological invariants of time-reversal-invariant band structures
• Edge states and topological invariants of non-Hermitian systems
• Quantized Electric Multipole Insulators
• Exceptional Topology of Non-Hermitian Systems
• Non-Hermitian Physics
• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Higher-Order Topological Insulators
• Topological phases of non-Hermitian systems
• The physics of exceptional points
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Symmetry and Topology in Non-Hermitian Physics
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Anomalous edge state in a non-Hermitian lattice
• Reflection symmetric second-order topological insulators and superconductors
• PT-symmetry breaking and laser-absorber modes in optical scattering systems
• Non-Hermitian Chern bands
• Observation of bulk boundary correspondence breakdown in topolectrical circuits
• Pseudo-Hermiticity versus PT-Symmetry II: A complete characterizatio n of non-Hermitian Hamiltonians with a real spectrum
• Pseudo-Hermiticity versus PT-Symmetry III: Equivalence of pseudo-Her miticity and the presence of antilinear symmetries
• Three-Dimensional Topological Insulators
• PT-Symmetric Phonon Laser
• Classical higher-order topological insulators
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Edge states and topological phases in non-Hermitian systems
• Hybrid higher-order skin-topological modes in non-reciprocal systems
• Second-Order Topological Phases in Non-Hermitian Systems
• Metrology with $\mathcal{P}\mathcal{T}$-symmetric cavities: Enhanced sensitivity near the $\mathcal{P}\mathcal{T}$-phase transition
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Universal non-Hermitian skin effect in two and higher dimensions
• Classification of Exceptional Points and Non-Hermitian Topological Semimetals
• Non-Hermitian topological phenomena: A review
• Higher-order non-Hermitian skin effect
• Amorphous topological insulators constructed from random point sets
• Topological states of non-Hermitian systems
• Surface State Magnetization and Chiral Edge States on Topological Insulators
• Non-Hermitian perspective of the band structure in heavy-fermion systems
• Topological unification of time-reversal and particle-hole symmetries in non-Hermitian physics
• Quantum Oscillation from In-gap States and non-Hermitian Landau Level Problem
• Non-Hermitian Localization and Population Biology
• Symmetry-protected nodal phases in non-Hermitian systems
• Higher-Order Topological Insulators in Quasicrystals
• Topological Insulators in Random Lattices
• Second-order topological non-Hermitian skin effects
• Flat Band in Disorder Driven Non-Hermitian Weyl Semimetals
• Non-Hermitian route to higher-order topology in an acoustic crystal
• Chiral Coherent Perfect Absorption on Exceptional Surfaces
• Topological phases without crystalline counterparts
• Higher-order topological insulators in amorphous solids
• Simulating non-Hermitian quasicrystals with single-photon quantum walks
• Nodal Arc in Disordered Dirac Fermions: Connection to Non-Hermitian Band Theory
• Exceptional Points in Random-Defect Phonon Lasers
• Non-Hermitian Localization in Biological Networks
• Hyperbolic Matter in Electrical Circuits with Tunable Complex Phases
• Non-Hermitian topology of spontaneous magnon decay
• Time-Reversal Symmetry in Non-Hermitian Systems
• Enhancement of Second-Order Non-Hermitian Skin Effect by Magnetic Fields
• Dynamically crossing diabolic points while encircling exceptional curves: A programmable symmetric-asymmetric multimode switch
• Topologically protected modes in non-equilibrium stochastic systems
• Non-Hermitian Topological Phases: Principles and Prospects
• Floquet second-order topological insulators in non-Hermitian systems
• Non-Hermitian higher-order topological superconductors in two-dimension: statics and dynamics
• Damped Dirac magnon in a metallic kagome antiferromagnet FeSn
• Non-Hermitian Absorption Spectroscopy
• Stable Atomic Magnetometer in Parity-Time Symmetry Broken Phase
• Real spectra in non-Hermitian topological insulators
• Disorder-induced exceptional and hybrid rings in Weyl/Dirac semimetals
• Evidencing non-Bloch dynamics in temporal topolectrical circuits
• Dynamical signatures of point-gap Weyl semimetal
• Mesoscopic transport signatures of disorder-induced non-Hermitian phases
• Exceptional Heavy-Fermion Semimetals in Three Dimensions

Cited by in corpus (8)

• Non-Hermitian Second-Order Topological Phases and Bipolar Skin Effect in Photonic Kagome Crystals
• Corner modes in non-Hermitian next-nearest-neighbor hopping model
• Quasiparticle picture of topological phase transitions induced by interactions
• Interplay of non-Hermitian skin effect and electronic correlations in the non-Hermitian Hubbard model via Real-space dynamical mean field theory
• Superconducting order parameter in aperiodic binary systems
• Non-Hermitian second-order topological insulator with point gap
• Quasiperiodic Skin Criticality in an Exactly Solvable Non-Hermitian Quasicrystal
• Generic non-Hermitian mobility edges in a class of duality-breaking quasicrystals