Fig. 1: Schematic of the physics and the reported MEMS device, aided by theoretical and experimental results. | Nature Communications

Fig. 1: Schematic of the physics and the reported MEMS device, aided by theoretical and experimental results.

From: Localized topological states beyond Fano resonances via counter-propagating wave mode conversion in piezoelectric microelectromechanical devices

Fig. 1: Schematic of the physics and the reported MEMS device, aided by theoretical and experimental results.

a Strong wave localization is achieved by leveraging the interference of two topologically protected localized states, named as State-1 and State-2. b This scenario differs from the conventional Fano resonance, wherein the dark and bright states have very different lifetimes, i.e. the bright state approaches a continuum state and the dark mode is a localized state. c 3D rendering of the schematized topological problem: the interference between State-1 and State-2 is described by coupling, at a topological interface, counter-propagating symmetric (S0) (red) and antisymmetric (A0) (blue) Lamb waves each with distinct Zak phases. d Such wave coupling is achieved, in one-dimensional wave propagation, by breaking the horizontal spatial symmetry, i.e. by corrugating one side of the surface of an elastic plate. This structure is then combined with an elastic version of the SSH model, where an interface is encountered between two periodic structures (C1 and \({{\rm{C}}}{1}^{{\prime} }\)). The unit cells of each structure shares the same periodicity a, but have corrugated elements separated by Δ and a − Δ respectively. This creates two topological interface states with distinct Zak phases and different wavenumbers, as shown by the 2D Fast Fourier Transform of wavefield from numerical simulations. Refer to Table S1 in the supplementary material for a description of all variables included in the plot. e We report a piezoelectric MEMS prototype using Aluminum Scandium Nitride as a piezoelectric material, Silicon Oxide to form the periodic corrugations of C1 and \({{\rm{C}}}{1}^{{\prime} }\), and Aluminum strips to form the electrical ports. f The experimental electrical transmission of this MEMS device, expressed in terms of the S21 scattering parameter, shows the existence of two interface states that lie within a complete bandgap. At their destructive interference, marked with a red star, strong localization is achieved, as well as a record-high Q for MEMS devices using AlScN films as piezoelectric layers.

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