This conference presentation was prepared for the Active and Passive Smart Structures and Integrated Systems XVII conference at SPIE Smart Structures + Nondestructive Evaluation, 2023
The Z2 invariant associated with quantum spin Hall topological insulators is connected to the unique property of fermionic systems whose wavefunction acquires a negative sign upon two consecutive applications of the time-reversal operator. However, this property is not acquired by the classical-wave systems. Instead, a combination of spatial and temporal symmetry is required to synthesize the Kramers degeneracy. In this study, we propose an elastic phononic plate engraved with a honeycomb lattice whose depth varies according to a Kekule pattern. The “local topological charge” can be defined based on the difference of integrated pseudospin-resolved Berry curvature profiles, as an alternative to the Z2 invariant. Such “local topological charge” is not a topological invariant in a rigorous sense, since it depends on the position of the reference frame. This condition also leads to the result that the same phononic structure can be in different topological phases based on different reference frames. It follows that edge states can exist on a dislocation interface connecting two pieces of the same phononic structure with relative shifting. Two pseudospin-polarized edge-state bands crossing at zero-k point (synthetic Kramers pair) are achieved without repulsion, hence indicating decoupling and robustness of the counter-propagating states.
We experimentally demonstrate the existence and the characteristics of acoustic quantum valley Hall edge states in a continuous topological elastic waveguide. The waveguide is obtained by subtractive manufacturing, hence cutting a non-resonant truss-like lattice from an initially uniform aluminum thin plate. The fabricated lattice includes two different domains characterized by broken space inversion symmetry and contrasted with each other in order to create a physical interface (i.e. a domain wall) capable of inducing a topological transition. Guided modes in the waveguide are generated using piezoelectric actuators and are measured using laser vibrometry. Data show the existence of well-confined edge states with negligible backscattering at the sharp corners along the domain wall. A methodology to precisely excite a uni-directional edge state is also demonstrated. In addition to the experiment results, the coupling between valley modes is also further investigated and linked to a chiral flux of the mechanical energy.
We study a continuous phononic elastic structure capable of reconfigurable topological edge states. The occurrence of edge states is due to a mechanism that can be considered as the acoustic analogue of the quantum valley Hall effect. By assembling two lattices having broken space-inversion-symmetry we induce gapless edge states at the corresponding domain wall, that is the interface between the lattices. The spatial symmetry of the phononic lattice as well as the topological transition are controlled by an externally imposed strain field. The underlying physical mechanism controlling the propagation behavior in such phononic structure is investigated by a combination of theoretical analyses and numerical simulations. Results show that chiral edge states can be obtained at the domain wall and that the strain field enables their direct tuning. Although this approach produces only a weak topological material in which time-reversal symmetry is still intact, the edge states supported at the domain wall prove to be very robust against back-scattering, even in presence of strong lattice disorder.
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