Edge waves in plates with resonators: an elastic analogue of the quantum valley Hall effect

Abstract

We investigate elastic periodic structures characterized by topologically nontrivial bandgaps supporting backscattering suppressed edge waves. These edge waves are topologically protected and are obtained by breaking inversion symmetry within the unit cell. Examples for discrete one and twodimensional lattices elucidate the concept and illustrate parallels with the quantum valley Hall effect. The concept is implemented on an elastic plate featuring an array of resonators arranged according to a hexagonal topology. The resulting continuous structures have non-trivial bandgaps supporting edge waves at the interface between two media with different topological invariants. The topological properties of the considered configurations are predicted by unit cell and finite strip dispersion analyses. Numerical simulations demonstrate edge wave propagation for excitation at frequencies belonging to the bulk bandgaps. The considered plate configurations define a framework for the implementation of topological concepts on continuous elastic structures of potential engineering relevance.

Snowflake phononic topological insulator at the nanoscale

“…So far, experimental implementations exist on the centimeter scale, both for the case of time-reversal symmetry broken by external driving [1], such as in coupled gyroscopes, as well as for the case without driving [2][3][4][5][6], such as in coupled pendula. Moreover, a multitude of different implementations have been envisioned theoretically [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. However, it is highly desirable to come up with alternative design ideas that may be realized on the nanoscale, eventually pushing towards applications in integrated phononics.…”

Tunable Acoustic Valley–Hall Edge States in Reconfigurable Phononic Elastic Waveguides

“…However, due to the large separation in k-space of the two valleys, valley-dependent topological invariants can be defined and used to classify the topological states of the different lattices. This approach, usually referred to as quantum valley Hall effect (QVHE), was recently investigated for application to fluidic acoustic waveguides 9,12 , as well as elastic plates with local resonators 28,29 .…”

“…1(a)). Compared to the previous studies 28, 29 , we take a fully continuum modeling approach which provides a general methodology of analysis and allows mapping the topological behavior all the way back to the massless (or massive when SIS is broken) Dirac equation. Also, an in-depth study of the occurrence of edge states, either at domain walls or at the lattice boundaries, is presented.…”

Valley‐Hall Photonic Topological Insulators with Dual‐Band Kink States

“…Over the past few years, “valleytronics” has emerged as an area where valley, a binary degree of freedom, has a potential to be an excellent candidate of information carrier. The concept of valley has also been introduced into different kinds of physical systems, such as photonics, acoustics, and elastics . In the photonic community, researchers have found that domain walls between two types of inversion‐breaking photonic crystals, that is, valley‐Hall photonic topological insulators (PTIs), could support topologically nontrivial valley‐polarized kink states.…”