Session: 01-02-01: Topological Phononics

Paper Number: 173103

Unconventional Edge States in Phononic Crystals With Long-Range Coupling 

As a special class of mechanical metamaterials and phononic crystals, topological mechanical metamaterials and phononic crystals with unusual wave control abilities have gained significant attention over the past decade. Similar to topological insulators in quantum physics, where a topological invariant is used to categorize materials or structures with similar conductive states, in mechanical systems, such an invariant can also be derived from the spectral evolution of eigenvectors or mode shapes obtained from a unit cell analysis. This helps determine the number and types of topologically protected edge states that confine phonon modes both statically and dynamically, usually known as the bulk-edge correspondence.

A typical process to create topological mechanical metamaterials and phononic crystals involves: 1) starting with a symmetric lattice, 2) finding the Dirac point, 3) breaking the lattice symmetry, and 4) checking if the resulting bandgap is topological or trivial by identifying the topological invariants. We can see from this process that opening a bandgap is crucial for creating topological states at the domain boundary. However, the decay rate of these protected edge or boundary states into the bulk depends on the size of the bandgap. When the bandgap is large, the spatial decay of the topologically protected edge state is rapid, but high symmetry breaking may cause inter-valley mixing due to significant symmetry perturbation. This complicates the calculation of the topological invariant, which may not be an integer. On the other hand, when the perturbation is small, the bandgap is small, and the topologically protected edge state decays slowly into the bulk, making it hard to observe if the finite lattice size is similar to the decay length. In this work, we avoid such bandgap-related issues by introducing a new class of nontrivial edge states that follow the bulk-boundary correspondence without the need for bulk bandgap opening or topological invariants. As a result, symmetry breaking along the lattice vector is not necessary to produce edge states. These edge states occur at energies corresponding to quantum numbers where additional stationary points appear in the continuum phonon dispersion of the related problem with periodic boundary conditions. We will demonstrate these phenomena using a phononic crystal lattice with next-nearest-neighbor coupling. It is also worth noting that defects and additional local constraints are not required to create such edge states in the bulk mode, as studied by previous researchers.

In this presentation, we will systematically explore these boundary states through a combination of theoretical analysis, finite element analysis, and laser-assisted experimental characterization using a scanning laser Doppler vibrometer, based on successful predictions of boundary states in the bulk through 3D-printed quasi-one-dimensional metamaterials.

Presenting Author: Jihong Ma University of Vermont

Presenting Author Biography: Jihong Ma is a tenure-track Assistant Professor in the Department of Mechanical Engineering at the University of Vermont (UVM). Dr. Ma obtained her Ph.D. in Mechanical Engineering from the University of Minnesota-Twin Cities in 2017 and her B.Eng. in Engineering Mechanics from Xi'an Jiaotong University (China) in 2012. Her Ph.D. thesis focused on computational heat transport in nanomaterials. She then worked as a Postdoctoral Associate in the Department of Civil, Environmental, and Geo- Engineering at the University of Minnesota-Twin Cities, studying topological metamaterials from 2017 to 2019, and at Oak Ridge National Laboratory - Center for Nanophase Materials Sciences on soft matter simulations.

Authors:

Amir Rajabpoor Alisepahi University of Vermont
Charles Downing University of Exeter
Jihong Ma University of Vermont