Topological Boundary Modes from Translational Deformations

Abstract

Localized states universally appear when a periodic potential is perturbed by defects or terminated at its surface. In this Letter, we theoretically and experimentally demonstrate a mechanism that generates localized states through continuous translational deformations of periodic potentials. We provide a rigorous proof of the emergence of the localized states under the deformations. The mechanism is experimentally verified in microwave photonic crystals. We also demonstrate topological phase windings of reflected waves for translated photonic crystals.

arXiv comment11 pages, 13 figures

References in corpus (11)

• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Topological Insulators in Three Dimensions
• Topological Photonics
• Classification of topological insulators and superconductors in three spatial dimensions
• Surface Impedance and Bulk Band Geometric Phases in One-Dimensional Systems
• Optical Tamm states in one-dimensional magnetophotonic structures
• Induced transparency by coupling of Tamm and defect states in tunable terahertz plasmonic crystals
• Localized end states in density modulated quantum wires and rings
• Fractional boundary charges in quantum dot arrays with density modulation
• From fractional boundary charges to quantized Hall conductance

Cited by in corpus (8)

• Non-Hermitian waves in a continuous periodic model and application to photonic crystals
• Second Chern crystals in four-dimensional synthetic translation space with inherently nontrivial topology
• Polaritonic Tamm states induced by cavity photons
• Observation of gapless corner modes in synthetic translation dimensions
• Homogeneous Dislocation-Induced Rainbow Concentrating for Elastic Waves
• Universal properties of boundary and interface charges in continuum models of one-dimensional insulators
• Multi-dimensional wave steering with higher-order topological phononic crystal
• Internal wave crystals