The kagome lattice, named after the pattern of a Japanese woven basket, draws the attention of physicists because of its unusual electronic properties: flat bands, Dirac cones, and van Hove singularities. In materials such as AV₃Sb₅, these features are linked to superconductivity and charge density waves. However, direct experimental confirmation of how the wave function is distributed across the three sublattices remained a hard problem. Electronic methods, such as photoemission spectroscopy, are not sensitive to the phase of Bloch electrons, and real crystals are often too complex because of multiorbital character and three-dimensional surroundings. Acoustic metamaterials offer a clean platform where the Hamiltonian is encoded in the lattice geometry, and they allow the field to be measured at every node. This work sits alongside studies of topological states in metamaterials, but it stands out for its focus on the sublattice structure, which had not been observed directly before.
The authors 3D-printed an acoustic kagome lattice with a lattice constant of 28 mm. Each node consists of three resonators (sublattices A, B, C) surrounding a central cavity H. A speaker with a 1 mm aperture was placed in a node of a chosen sublattice and emitted a sinusoidal signal with a linear frequency sweep from 100 to 12000 Hz over 30 seconds. A microphone on a robotic arm sequentially scanned all nodes, recording the complex response (amplitude and phase). Measurements were repeated for each of the three sublattices. Then real space was transformed into momentum space using a two-dimensional discrete Fourier transform, yielding dispersion relations and the intensity distribution across the Brillouin zone. For interpretation, a minimal tight-binding model with a single hopping parameter t and an on-site energy ε₀ was used.
The experimental band structure reproduces the characteristic features of the kagome lattice beautifully: two van Hove singularities at 5.5 kHz and 8.0 kHz, a Dirac cone near 6.7 kHz, and a flat band at 10.9 kHz. The fit gave t = 1.4 kHz and ε₀ = 8.05 kHz. At low frequencies the dispersion is linear, which corresponds to the long-wavelength limit, where sound perceives the lattice as a continuous medium with an effective speed of ~256 m/s. Near the Brillouin zone boundaries, the spectrum matches the tight-binding model. Mapping the sublattice character of the flat band revealed a cyclic change in composition: A → AB → B → BC → C → CA → A along the Γ–K and Γ–M directions. In real space, at the flat-band frequency, the wave is localized on two neighboring rings, and adjacent resonators oscillate in antiphase (a shift of π), which directly confirms the destructive interference mechanism. For the van Hove singularities, the lower one (5.5 kHz) was found to be of mixed type with sublattice pairs, while the upper one (8.0 kHz) is of pure type with one sublattice dominating. Fourier filtering at selected M points showed that in real space the amplitude is strictly confined to the expected sublattices: for the p-type, only sublattice B lights up; for the m-type, A and C do, forming chains at an angle of 150° with interference fringes.
The work provides the first direct experimental evidence of the sublattice texture of the kagome band structure, including phase information that is inaccessible to electronic methods. Unlike neighboring metamaterial studies that focused on topological edge states or the skin effect, this one measured the sublattice polarization of the wave function across the entire Brillouin zone. This confirms theoretical predictions about the role of sublattices in correlation effects and provides a benchmark for interpreting data from complex electronic materials. It is shown that the anisotropic distribution of spectral weight on the flat band can serve as an indicator of its kagome origin, distinguishing it from trivially localized d- or f-orbitals.
The acoustic platform, with full access to phase and amplitude, opens the way to systematic studies of sublattice effects in other geometries: pyrochlore, dimer lattices, and models with long-range hopping. Controlled perturbations can be introduced, for example, by changing the coupling to cavity H or adding dissipation, and one can observe how this affects flat bands and singularities. Extending the approach to non-Hermitian systems and topological phases, where the phase structure of the wave function plays a key role, is a promising direction.
The results are useful for interpreting experiments in electronic kagome materials such as AV₃Sb₅, where the sublattice structure may determine the mechanisms of superconductivity and charge density waves. The methodology is also applicable to designing acoustic and photonic devices with tailored localization and interference properties.
The immediate next step is a quantitative comparison with a four-band model that includes weak coupling to cavity H, along with systematic variations of the geometry to identify the role of this cavity. It is also important to study how dissipation affects the dispersion of the flat band and its sublattice composition.
In condensed matter physics, a question remains open: how does the sublattice structure of flat bands and van Hove singularities influence the emergence of superconductivity and charge density waves in kagome metals? This work provides a direct experimental method for testing theoretical models of correlation effects that depend on the type of sublattice polarization (pure or mixed).
This section is addressed to the author of the paper and their colleagues. Neighbouring works were found by meaning-based search across our archive, not by word overlap. We do not review: we show the field around the work.
What the work does
The authors built an acoustic analogue of a kagome lattice and measured the complex sound field at each node, reconstructing the band structure and the sublattice distribution of the wave function. They showed that the lower van Hove singularity is mixed, the upper one is pure, and the flat band arises from destructive interference.
Where its strength is
Direct mapping of the sublattice character of the states, including phase, offers a unique opportunity to visualize mechanisms that are hidden in electronic materials.
Where it could go next
Worth trying
Why this may matter
Such model systems allow theoretical predictions for quantum materials to be tested under controlled conditions, which could speed up the search for new functional materials.
Nearby works in our archive
The archive is sparse around this work: the closest review is only 0.52, against a usual 0.64. It looks like few have drilled nearby.
The name "kagome" comes from the pattern of a Japanese woven basket, where triangles and hexagons alternate just as they do in this lattice. In the experiment, the lattice constant is 28 mm, and the frequencies lie in the audible range: the flat band at 10.9 kHz is a high but discernible whistle.