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Supersolids are a remarkable state of matter, exhibiting both superfluidity and crystalline properties. We predict a rich excitation spectrum for a binary dipolar supersolid in a linear crystal geometry, where the ground state consists of two partially immiscible components forming alternating, interlocking domains. We identify three Goldstone branches, each exhibiting first-sound, second-sound, or spin-sound character. By analogy with a diatomic crystal, the resulting lattice has a two-domain primitive basis, and we find that the crystal (first-sound-like) branch splits into optical and acoustic phonons. Additionally, we identify a spin-Higgs branch associated with the supersolid modulation amplitude [1].
[1] W. Kirkby, Au-Chen Lee, D. Baillie, T. Bland, F. Ferlaino, P. B. Blakie, R. N. Bisset, Phys. Rev. Lett. ${\textbf 133}$, 103401 (2024)
