A new class of higher-order topological insulators that localize energy at arbitrary multiple sites

Abstract

$\mathbb{Z}$-classified topological phases lead to larger-than-unity topological states. However, these multiple topological states are only localized at the corners in nonlocal systems. Here, first, we rigorously prove that the multiple topological states of nonlocal Su-Schrieffer-Heeger (SSH) chains can be inherited and realized by local aperiodic chains with only the nearest couplings. Then, we report a new class of higher-order topological insulators constructed with the local aperiodic chains, which can have any integer number of 0D topological states localized at arbitrary positions in the whole domain of the insulators, including within the bulk. The 0D topological states are protected by the local topological marker in each direction, instead of the bulk multipole chiral numbers in the existing work. Our work provides multiple combinations of localized corner-bulk topological states, which enables programmable lasers and sasers by selecting the excitation sites without altering the structure, and thus opens a new avenue to signal enhancement for computing and sensing.

References in corpus (40)

• Topological Insulators
• Topological insulators and superconductors
• Weyl and Dirac Semimetals in Three Dimensional Solids
• Photonic Floquet Topological Insulators
• Classification of topological quantum matter with symmetries
• Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry
• Quantized Electric Multipole Insulators
• Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices
• Novel Topological Phase with Zero Berry Curvature
• Observation of second-order topological insulators in sonic crystals
• Topological acoustics
• Elastic higher-order topological insulator with topologically protected corner states
• Topological phases of generalized Su-Schrieffer-Heeger models
• Low-threshold topological nanolasers based on second-order corner state
• Non-Hermitian Morphing of Topological Modes
• Nonlinear second-order photonic topological insulators
• Lasing from multipole topological corner states
• Dimensional hierarchy of higher-order topology in three-dimensional sonic crystals
• Topological characterization of chiral models through their long time dynamics
• Actively controllable topological phase transition in phononic beam systems
• Edge states and topological pumping in elastic lattices with periodically modulated coupling
• Interplay between long range hopping and disorder in topological systems
• Observation of Acoustic Non-Hermitian Bloch Braids and Associated Topological Phase Transitions
• Coupled-wire construction of static and Floquet second-order topological insulators
• Chiral-Symmetric Higher-Order Topological Phases of Matter
• Experimentally Detecting Quantized Zak Phases without Chiral Symmetry in Photonic Lattices
• Higher-order topological phases on fractal lattices
• Sub-symmetry protected topological states
• Observation of degenerate zero-energy topological states at disclinations in an acoustic lattice
• A two-leg Su-Schrieffer-Heeger chain with glide reflection symmetry
• An elementary rigorous proof of bulk-boundary correspondence in the generalized Su-Schrieffer-Heeger model
• Non-Hermitian engineering of single mode two dimensional laser arrays
• Topological origin of edge states in two-dimensional inversion-symmetric insulators and semimetals
• Realization of a Z classified chiral-symmetric higher-order topological insulator in a coupling-inversion acoustic crystal
• Non-Local Phononic Crystals for Dispersion Customization and Undulation-point Dynamics
• Higher-order topological states mediated by long-range coupling in $D_4$-symmetric lattices
• Spinful topological phases in acoustic crystals with projective PT symmetry
• Smart patterning for topological pumping of elastic surface waves
• Long-range hopping and indexing assumption in one-dimensional topological insulators
• Higher-order topological insulator in a modified Haldane-Hubbard model