[Paper Review] Interface states in two-dimensional quasicrystals with broken inversion symmetry

Danilo Beli, Matheus I. N. Rosa+3 more|arXiv (Cornell University)|Apr 19, 2023

Quasicrystal Structures and PropertiesMaterials Science3 citations

TL;DR

This paper proposes a mechanism to induce topological interface states in two-dimensional quasicrystals by breaking inversion symmetry via mass dimerization, creating 10-fold symmetric lattices with two 5-fold sub-lattices. The method enables robust, backscattering-free waveguiding along zig-zag interfaces with 36° turns—exceeding the 60° limit of conventional honeycomb lattices—demonstrated both numerically and experimentally in elastic plates with localized interface modes at 6950 Hz.

ABSTRACT

We investigate the existence of interface states induced by broken inversion symmetries in two-dimensional quasicrystal lattices. We introduce a 10-fold rotationally symmetric quasicrystal lattice whose inversion symmetry is broken through a mass dimerization that produces two 5-fold symmetric sub-lattices. By considering resonator scatterers attached to an elastic plate, we illustrate the emergence of bands of interface states that accompany a band inversion of the quasicrystal spectrum as a function of the dimerization parameter. These bands are filled by modes which are localized along domain-wall interfaces separating regions of opposite inversion symmetry. These features draw parallels to the dynamic behavior of topological interface states in the context of the valley Hall effect, which has been so far limited to periodic lattices. We numerically and experimentally demonstrate wave-guiding in a quasicrystal lattice featuring a zig-zag interface with sharp turns of 36 degrees, which goes beyond the limitation of 60 degrees associated with 6-fold symmetric (i.e., honeycomb) periodic lattices. Our results provide new opportunities for symmetry-based quasicrystalline topological waveguides that do not require time-reversal symmetry breaking, and that allow for higher freedom in the design of their waveguiding trajectories by leveraging higher-order rotational symmetries.

Motivation & Objective

• To extend topological waveguiding mechanisms from periodic lattices to quasicrystalline systems with higher rotational symmetries.
• To investigate whether interface states can emerge in passive, time-reversal-symmetric quasicrystals through inversion symmetry breaking alone.
• To demonstrate waveguiding with sharp angular turns (36°) in quasicrystalline lattices, surpassing the 60° limit of conventional 6-fold periodic systems.
• To provide a design framework for symmetry-based topological waveguides without requiring magnetic fields or active components.
• To validate the existence of topologically protected interface states in quasicrystalline elastic metamaterials through numerical simulations and experimental measurements.

Proposed method

• Engineered a 10-fold rotationally symmetric quasicrystal lattice with dimerized masses to break inversion symmetry, forming two 5-fold sub-lattices.
• Used resonator scatterers attached to an elastic plate to realize the quasicrystalline lattice and simulate its vibrational band structure.
• Varied the dimerization parameter to induce a band inversion in the quasicrystal spectrum, signaling topological transition.
• Performed numerical simulations using finite element methods to predict interface state formation at domain walls between regions of opposite inversion symmetry.
• Fabricated a 3D-printed quasicrystalline plate with a zig-zag interface and experimentally measured its frequency response using a scanning laser Doppler vibrometer.
• Excited the system with a sinusoidal wavepacket at 6950 Hz and recorded transient wave propagation to confirm unidirectional, backscattering-free transport along the interface.

Experimental results

Research questions

• RQ1 Can topological interface states emerge in two-dimensional quasicrystals through inversion symmetry breaking alone, without time-reversal symmetry breaking or external fields?
• RQ2 Does the higher rotational symmetry (10-fold) in quasicrystals enable waveguiding with sharper turns than those possible in 6-fold periodic lattices?
• RQ3 How does band inversion in the quasicrystal spectrum correlate with the emergence of localized interface states?
• RQ4 To what extent do interface states in quasicrystals exhibit robustness against defects and sharp geometric features such as 36° corners?
• RQ5 Can the valley Hall effect-like behavior observed in periodic lattices be generalized to quasicrystalline systems through symmetry engineering?

Key findings

• A band inversion was observed in the quasicrystal spectrum as a function of the dimerization parameter, indicating a topological transition.
• Interface states emerged as localized modes along domain walls separating regions of opposite inversion symmetry, confirmed by both simulations and experiments.
• The interface state was experimentally observed at a resonance frequency of 6950 Hz, with energy concentrated along the zig-zag interface and minimal spatial decay.
• Wave propagation along the interface was demonstrated via transient response, showing unidirectional, backscattering-free transport through 36° angular turns.
• The system exhibited significant spatial attenuation due to material dissipation, but the interface mode remained clearly localized and guided.
• The results confirm that topological waveguiding in quasicrystals can be achieved through simple inversion symmetry breaking, enabling new design freedom in waveguide trajectories.