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

Abstract

This study investigates the occurrence of acoustic topological edge states in a 2D phononic elastic waveguide due to a phenomenon that is the acoustic analogue of the quantum valley Hall effect. We show that a topological transition takes place between two lattices having broken space inversion symmetry due to the application of a tunable strain field. This condition leads to the formation of gapless edge states at the domain walls, as further illustrated by the analysis of the bulk-edge correspondence and of the associated topological invariants. Although time reversal symmetry is still intact in these systems, the edge states are topologically protected when inter-valley mixing is either weak or negligible. Interestingly, topological edge states can also be triggered at the boundary of a single domain if boundary conditions are properly selected. We also show that the static modulation of the strain field allows tuning the response of the material between the different supported edge states.

Acoustic graphene network loaded with Helmholtz resonators: a first-principle modeling, Dirac cones, edge and interface waves

“…The blue solid lines represent the analytical results from equation (7) for ε B =ε g (no resonator), and the black dot lines the finite element simulation. As it can be seen, the degeneracy of the Dirac point at the K point is lifted creating a band-gap, due to inversion symmetry breaking, similar to other inversion symmetry breaking systems [5,7,23,31]. On the other hand, a unique feature of our system is the appearance of an additional nearly flat band inside the generated band gap around the resonance frequency f A .…”

“…It should be mentioned that the common approach to get dispersion curves by sweeping Bloch wave vector in the BZ is not suitable in our system when HRs are loaded to junction A of the network. The challenge is that the energy term ε A (equation (5)) contains the contribution part of the resonator G A , while ε B is not affected by resonance, leading to the breakdown of the eigenvalue problem of the form shown in equation (5). However, the eigenvalue equation (10) avoids the obstacle caused by resonance since its eigenvalue gives rise to the Bloch wave vector.…”

“…As it has been studied in the analogs of QVH system [5,7,23,31], the interface modes in the full gap appearing by breaking the Dirac cone at the K point are robust in a sense that they can travel through corners of 120 • with respect to its original direction of propagation. This phenomenon can also be observed in our SLGN.…”

“…Over the last years, in the context of metamaterials, a plethora of sophisticated acoustic structures exhibiting unusual wave properties have been theoretically proposed and also experimentally studied. Examples include Dirac cones [1], unidirectional propagation [2][3][4], topological interface waves [5][6][7], robust localized modes [8], etc. Recently periodic acoustic/elastic media have been proven to be an excellent platform for studying various wave phenomena [9].…”

2D Phononic Crystals: Progress and Prospects in Hypersound and Thermal Transport Engineering

“…Breaking the time‐reversal symmetry to obtain an equivalent to the quantum Hall effect in bosonic lossless systems requires active materials responding to an external field, a nonlinearity, or time‐dependent physical properties, which in the case of elasticity is especially difficult. Therefore, several proposals, as well as few experimental realizations, have achieved topological phenomena by emulating the quantum spin Hall effect or quantum valley Hall effect in passive linear structures. While conserving time‐reversal symmetry, these topological structures are based on breaking some spatial inversion symmetry.…”