Fig. 5: Observation of topology using a spectrally localized acoustic metamaterial.
From: Revealing topology in metals using experimental protocols inspired by K-theory
a Photograph of the fully assembled spectrally localized metamaterial with the added sublattice-dependent on-site energies to the underlying metallized SSH lattice. The resonators that comprise this system can be re-assembled to realize different choices of the center of the localized potential x in Eq. (6). b COMSOL simulated resonant spectrum of the spectrally localized metamaterial as the position of the localized potential’s center x is varied, demonstrating the existence of the two bands in the dynamical localization gap. c,d,e Localizer index (c), localizer gap (d), and secondary gaps (e) derived from the full-wave simulated spectrum. The localizer index and gap are calculated using the mid-spectrum frequency indicated in b (blue arrow on right), and the two frequencies chosen for calculating the secondary gaps are similarly indicated (cyan and magenta arrows on right). f Experimental mapping of the local density of states as the localized potential’s center is moved (constructed from microphone readings on the dimer where the localized potential is centered x), confirming the existence of the two central eigenvalues for varying x seen in b. α = 2.5a and κ = 1.85 kHz2 in Eq. (6) were used in our simulations and experiments, where a is the lattice constant. The observed pressure amplitude ∣p∣ is shown in normalized units. g Measured pressure in normalized units for the spectrally localized system’s bulk eigenvalues constructed from the microphone readings on the bulk resonators at least 3 resonators away from the localized potential center. The gray lines in f and g are showing that the spectrally localized system’s two central sets of eigenvalues are well separated from the system’s remaining eigenvalues. h Experimentally measured mode profiles at 4760 Hz and 4860 Hz when x = 0 using the same color map as f. The red and blue triangles in b and f correspond to the frequency and localized potential center chosen for observing these data.
