Topological Classical Systems with Generalized Chiral Symmetry

Abstract

The bulk band topology of symmetry invariant adiabatic systems in the thermodynamic limit are considered to be determined by the hopping energy. In this work, we present that in closed classical systems, due to generalized chiral symmetry broken, the on-site energy cannot always be regarded as identical and can crucially impact the topological properties of the systems. Based on a finite one-dimensional chain, we demonstrate that the non-equivalent on-site energy of bulk lattices affects the topological phases of the bands, and the on-site energy of end lattices affects the existence of the topological states. Along these lines, the correspondence with generalized chiral symmetry in acoustic system is rigorously proposed. Our work provides a new degree of freedom for topological classical systems, and can be generalized to higher-dimensions and non-Hermitian conditions.

arXiv comment17 pages, 5 figures

References in corpus (59)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect in Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Topological Photonics
• Topological Photonics
• Photonic Floquet Topological Insulators
• Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry
• Quantized Anomalous Hall Effect in Magnetic Topological Insulators
• Topological Crystalline Insulators
• Quantized Electric Multipole Insulators
• Photonic Analogue of Two-dimensional Topological Insulators and Helical One-Way Edge Transport in Bi-Anisotropic Metamaterials
• Scheme to Achieve Silicon Topological Photonics
• Higher-Order Topological Insulators
• Robust optical delay lines via topological protection
• Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Topological Acoustics
• Acoustic topological insulator and robust one-way sound transport
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Topolectrical circuit realization of topological corner modes
• Observation of phononic helical edge states in a mechanical 'topological insulator'
• Reflection symmetric second-order topological insulators and superconductors
• Observation of a phononic quadrupole topological insulator
• Observation of topological valley transport of sound in sonic crystals
• Acoustic higher-order topological insulator on a Kagome lattice
• Demonstration of a quantized microwave quadrupole insulator with topologically protected corner states
• Topologically protected elastic waves in phononic metamaterials
• Quantization of fractional corner charge in $C_n$-symmetric higher-order topological crystalline insulators
• The space group classification of topological band insulators
• Topological classification of crystalline insulators through band structure combinatorics
• Floquet Topological Insulators for Sound
• Visualization of higher-order topological insulating phases in two-dimensional dielectric photonic crystals
• Direct observation of corner states in second-order topological photonic crystal slabs
• Topological protection of photonic mid-gap cavity modes
• Topologically-protected refraction of robust kink states in valley photonic crystals
• Surface Impedance and Bulk Band Geometric Phases in One-Dimensional Systems
• Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide
• Observation of photonic anomalous Floquet Topological Insulators
• Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
• Observation of second-order topological insulators in sonic crystals
• Topologically protected acoustic helical edge states and interface states in strongly coupled metamaterial ring lattices
• Topological negative refraction of surface acoustic waves in a Weyl phononic crystal
• Synthetic gauge fields and Weyl point in Time-Reversal Invariant Acoustic Systems
• Elastic higher-order topological insulator with topologically protected corner states
• Experimental Realization of Acoustic Chern Insulator
• Optical Resonator Analog of a Two-Dimensional Topological Insulator
• Acoustic realization of quadrupole topological insulators
• Observation of topological valley modes in an elastic hexagonal lattice
• Valley Topological Phases in Bilayer Sonic Crystals
• A fractional corner anomaly reveals higher-order topology
• Helical Topological Edge States in a Quadrupole Phase
• Non-linear second-order topological insulators
• Demonstration of a 3rd order hierarchy of higher order topological states in a three-dimensional acoustic metamaterial
• Dimensional hierarchy of higher-order topology in three-dimensional sonic crystals
• Bound states in the continuum of higher-order topological insulators
• Fractional corner charges in spin-orbit coupled crystals
• Edge-dependent topology in Kekulé lattices