Observation of Dispersion Anomalies by Design.

Abstract

Band structures encode electronic, optical, and acoustic properties of matter and can serve as an essential tool in material discovery and design. Dispersion anomalies- sharp, non-standard features in the frequency-wavenumber relation- have been historically correlated with phonon-electron coupling or long-range interaction. Here, through a combination of experimental, numerical, and analytical methods, it is shown how magnetic couplings can induce negative stiffness and sculpt dispersion relations to support zero-frequency phonon anomalies at arbitrary, non-zero wavenumbers. The approach enables the realization of complete wavenumber bandgaps without time-modulation, electron-phonon coupling, or long-range interactions. The conditions under which non-differentiable zero-frequency phonons exist away from the high-symmetry points are identified. The framework generalizes across monoatomic and diatomic lattices, locally resonant metamaterials, non-local systems, as well as higher dimensional crystals. In addition, the first- passive or active- experimental observation of wavenumber bandgaps in higher dimensions is reported. This work establishes a new paradigm in dispersion engineering and provides means for understanding wave-matter interaction in both the frequency and wavenumber domains.