Session: 13-02-02: Advances in the Mechanics of Architected Materials II

Paper Number: 166217

Class "A" Topological Acoustic Crystals: Capturing the Hofstadter Butterfly and Identifying Bulk and Edge Modes in a Coupled Resonator Lattice 

Topology provides a fundamental framework for understanding and classifying topological phases in acoustic metamaterials, enabling the realization of robust wave phenomena that persist in the presence of structural disorder. In this study, we computationally and experimentally investigate a reconfigurable two-dimensional (2D) acoustic lattice composed of H-shaped resonators, fabricated using high-precision 3D printing techniques. These resonators, designed to support tunable resonant frequencies, are coupled according to a quantum Hamiltonian, where the lattice configuration and quasi-periodicity govern the emergence of nontrivial topological phases. Our system falls within topological class A, meaning it is characterized by a nontrivial band structure without requiring additional symmetries such as time-reversal or particle-hole symmetry. This classification allows for the formation of topologically protected states, making it a suitable platform for exploring robust acoustic wave propagation.

The Hofstadter spectrum of the system was analyzed through three complementary approaches: (a) an analytical formulation derived from the proposed Hamiltonian, providing a theoretical representation of the energy spectrum; (b) computational simulations performed using COMSOL Multiphysics within the acoustic module, modeling a bilayer lattice composed of H-shaped resonators with cylindrical features to achieve a physical realization of the system; and (c) experimental measurements conducted on 3D-printed acoustic lattices, validating the theoretical and numerical predictions.

Computationally, we employ COMSOL Multiphysics using the acoustic module to model and analyze the system’s eigenfrequencies and wave propagation characteristics. The interplay between resonator geometry and coupling strengths facilitates the realization of a synthetic dimension, emulating topological bulk-boundary correspondence in virtual space. By introducing a phason degree of freedom into the Hamiltonian, we computationally map the Hofstadter butterfly spectrum and analyze the acoustic density of states as a function of frequency. The resulting energy spectrum exhibits a fractal structure, shaped by the interplay between hopping dimerization and the strength of the on-site potential.

The Hofstadter butterfly spectrum is represented by the eigenfrequencies (or eigenvalues) plotted as a function of the modulation phase θ, which serves as a phason in the Hamiltonian model. This modulation phase introduces an additional synthetic degree of freedom, allowing for the exploration of quasiperiodic structures with dynamic reconfigurability. The combination of analytical, computational, and experimental approaches provides a comprehensive understanding of the system’s topological characteristics, demonstrating the emergence of fractal spectral features and robust acoustic modes. These findings have significant implications for the development of topological acoustic platforms, with potential applications in quantum computing, where topologically protected modes provide a robust and error-resistant medium for quantum information processing.

Presenting Author: Koorosh Esteki Fordham University

Presenting Author Biography: Koorosh holds a Bachelor's degree in Mechanical Engineering and a Master of Science in Physics from the University of Lethbridge (2014). He earned his Ph.D. in Physics with a focus on Material Science in 2023. Since 2024, he has been a postdoctoral researcher at Fordham University, specializing in topological metamaterials.

Authors:

Koorosh Esteki Fordham University
Nicholas Patino University of Colorado Boulder
Curtis Rasmussen University of Colorado Boulder
Jackson Saunders Fordham University
Massimo Ruzzene University of Colorado Boulder
Emil Prodan Yeshiva University
Claudia Gomes Da Rocha University of Calgary
Camelia Prodan Fordham University