Topological phases of commensurate or incommensurate non-Hermitian Su-Schrieffer-Heeger lattices

Abstract

We theoretically investigate topological features of a one-dimensional Su-Schrieffer-Heeger lattice with modulating non-Hermitian on-site potentials containing four sublattices per unit cell. The lattice can be either commensurate or incommensurate. In the former case, the entire lattice can be mapped by supercells completely. While in the latter case, there are two extra lattice points, thereby making the last cell incomplete. We find that an anti-PT transition occurs at exceptional points of edge states at certain parameters, which does not coincide with the conventional topological phase transition characterized by the Berry phase, provided the imaginary on-site potential is large enough. Interestingly, when the potential exceeds a critical value, edge states appear even in the regime with a trivial Berry phase. To characterize these novel edge states we present topological invariants associated with the system's parity. Finally, we analyze the dynamics for initial states with different spatial distributions, which exhibit distinct dynamics for the commensurate and incommensurate cases, depending on the imaginary part of edge state energy.

arXiv comment10 pages, 8 figures

References in corpus (83)

• Topological insulators and superconductors
• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Topological Insulators with Inversion Symmetry
• Weyl Semimetal in a Topological Insulator Multilayer
• Edge states and topological invariants of non-Hermitian systems
• Dirac semimetal and topological phase transitions in A3Bi (A=Na, K, Rb)
• Complex Extension of Quantum Mechanics
• Exceptional Topology of Non-Hermitian Systems
• Non-Hermitian Physics
• Dirac semimetal in three dimensions
• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Three Dimensional Dirac Semimetal and Quantum Transports in Cd3As2
• Chern semi-metal and Quantized Anomalous Hall Effect in HgCr2Se4
• The physics of exceptional points
• Weyl semimetal phase in non-centrosymmetric transition metal monophosphides
• Symmetry and Topology in Non-Hermitian Physics
• Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Probing topological invariants in the bulk of a non-Hermitian optical system
• Non-Hermitian Topology and Exceptional-Point Geometries
• Selective enhancement of topologically induced interface states in a dielectric resonator chain
• Inversion Symmetric Topological Insulators
• Spectral equivalences, Bethe Ansatz equations, and reality properties in PT-symmetric quantum mechanics
• Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Biorthogonal Quantum Mechanics
• Edge states and topological phases in non-Hermitian systems
• Non-Hermitian Topological Invariants in Real Space
• Topologically protected midgap states in complex photonic lattices
• Non-Hermitian topological phenomena: A review
• Geometrical meaning of winding number and its characterization of topological phases in one-dimensional chiral non-Hermitian systems
• Topological Non-Hermitian skin effect
• Non-Hermitian skin modes induced by on-site dissipations and chiral tunneling effect
• Topological states of non-Hermitian systems
• Topological phases of generalized Su-Schrieffer-Heeger models
• Exceptional rings in two-dimensional correlated systems with chiral symmetry
• Absence of topological insulator phases in non-Hermitian PT-symmetric Hamiltonians
• PT-Symmetry in Non-Hermitian Su-Schrieffer-Heeger model with complex boundary potentials
• Topological invariance and global Berry phase in non-Hermitian systems
• Non-Bloch topological invariants in a non-Hermitian domain-wall system
• Non-Hermitian Hopf-Link Exceptional Line Semimetals
• Parity-time-symmetric topological superconductor
• Perspective on topological states of non-Hermitian lattices
• Anomalous Topological Phases and Unpaired Dirac Cones in Photonic Floquet Topological Insulators
• Non-Hermitian nodal-line semimetals with an anomalous bulk-boundary correspondence
• Effects of non-Hermitian perturbations on Weyl Hamiltonians with arbitrary topological charges
• PT-Symmetric Sinusoidal Optical Lattices at the Symmetry-Breaking Threshold
• Topological phases and edge states in a non-Hermitian trimerized optical lattice
• Knotted Non-Hermitian Metals
• Topological phase in a non-Hermitian PT symmetric system
• Non-Hermitian Topological Anderson Insulators
• Hall Conductance of a Non-Hermitian Chern Insulator
• Topological quantum wires with balanced gain and loss
• Topology of anti-parity-time-symmetric non-Hermitian Su-Schrieffer-Heeger model
• Majorana Modes in Driven-Dissipative Atomic Superfluids With Zero Chern Number
• Su-Schrieffer-Heeger chain with one pair of PT-symmetric defects
• Loss of Hall Conductivity Quantization in a Non-Hermitian Quantum Anomalous Hall Insulator
• Topological Bose-Mott insulators in one-dimensional non-Hermitian superlattices
• Non-Hermitian Topological Phases: Principles and Prospects
• Non-Hermitian band topology with generalized inversion symmetry
• Topology and Observables of the Non-Hermitian Chern Insulator
• Disorder-Induced Stabilization of the Pseudogap in Strongly Correlated Systems
• Fate of zero modes in a finite Su-Schrieffer-Heeger Model with $\mathcal{P}\mathcal{T}$ Symmetry
• The XXZ model with anti-periodic twisted boundary conditions
• Petermann factors and phase rigidities near exceptional points
• Inversion symmetric non-Hermitian Chern insulator
• Machine learning topological invariants of non-Hermitian systems
• Symmetry Indicators for Inversion-Symmetric Non-Hermitian Topological Band Structures
• Topological properties of subsystem-symmetry-protected edge states in an extended quasi-one-dimensional dimerized lattice
• Zeeman-field-induced nontrivial topological phases in a one-dimensional spin-orbit-coupled dimerized lattice
• Topological phases, topological flat bands, and topological excitations in a one-dimensional dimerized lattice with spin-orbit coupling
• Dynamical robustness of topological end states in nonreciprocal Su-Schrieffer-Heeger models with open boundary conditions
• Numerical calculation of the complex berry phase in non-Hermitian systems
• One-dimensional topological metal
• Breaking and resurgence of symmetry in the non-Hermitian Su-Schrieffer-Heeger model in photonic waveguides
• Dissipative Boundary State Preparation
• Topological properties of a generalized spin-orbit-coupled Su-Schrieffer-Heeger model
• Topological invariants for interacting systems: from twisted boundary condition to center-of-mass momentum
• Two-dimensional non-Hermitian topological phases induced by asymmetric hopping in a one-dimensional superlattice
• Symmetries and boundary conditions with a twist
• Detecting bulk and edge exceptional points in non-Hermitian systems through generalized Petermann factors
• Size and shape of Mott regions for fermionic atoms in a two-dimensional optical lattice
• Visualizing Topology of Real-Energy Gapless Phase Arising from Exceptional Point

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