Session: 01-02-01: Topological Phononics

Paper Number: 144375

144375 - Topological Bound Modes in Phononic Lattices With Nonlocal Interactions 

Elastic structures can be engineered to achieve tailored dispersion surfaces with nontrivial topological properties that allow extreme wave confinement and superior wave manipulation properties. Such properties, arising due to symmetry and topology of their dispersion surfaces, guarantee wave confinement or guiding even in presence of structural perturbations, such as geometrical and material changes or disorders. The rich symmetries of hexagonal lattices have enabled various topological modes, including chiral, helical, valley and higher order localized modes, under appropriate modifications.

In this work, discrete hexagonal lattices with distinct masses at sub-lattice sites and third nearest neighbor springs are considered. Each mass has one degree of freedom and can move out of plane. The dynamic behavior of the lattice is investigated from two aspects: the relative strength of the nearest neighbor and third-nearest neighbor springs, as well as the ratio of masses at the sub-lattice sites.

Our computations show that new Dirac cones arise above critical values of this ratio of nearest and third nearest neighbor spring stiffness, with a transition in their location as a function of this ratio. We then consider interfaces obtained between regions formed by two such lattices that are inverted copies of each other. These interfaces support two localized modes, associated with distinct nonzero valley Chern numbers of the lattices. For a specific type of interface satisfying a point reflection symmetry, the chain decouples into two identical copies at the high symmetry point of the Brillouin zone. This doubling guarantees the existence of two localized modes at the interface. Using a transfer matrix approach, explicit expressions for localized mode shapes at the high symmetry point are derived by exploiting symmetry. At a critical value of stiffness ratio, the two localized modes at the high symmetry point hybridize to give a bound mode, whose amplitude goes to zero outside a compact region. The existence of this bound mode is guaranteed by topological arguments, as the adjacent masses transition from moving in phase to out of phase across this critical value.

Finally, the use of third nearest neighbor connection was also demonstrated to be useful for a waveguiding application. This is done by considering a finite sample having a Z-shaped interface separating two lattices that are related by a point reflection symmetry. We numerically illustrate a sharp localization in the transverse direction of the waveguide associated with the bound mode. Our findings open novel avenues for topological wave guiding and confinement with potential applications in surface acoustic wave devices.

Presenting Author: Raj Kumar Pal Kansas State University

Presenting Author Biography: Raj Kumar Pal is an Assistant Professor in the Department of Mechanical and Nuclear Engineering at Kansas State University. His research interests are in the static and dynamic response of metamaterials.

Authors:

Vinicius Dal Poggetto Institut d’Electronique de Micro ́electronique et de Nanotechnologie
Marco Miniaci Institut d’Electronique de Micro ́electronique et de Nanotechnologie
Raj Kumar Pal Kansas State University