Collective Excitations and Stability of Nonequilibrium Polariton Supersolids

Original Abstract

Formation of nonequilibrium counterparts of supersolids, simultaneously characterized with spontaneous superfluid and crystalline order, was recently reported in incoherently pumped polariton condensates. We investigate collective excitation spectra of this phase and explicitly demonstrate the emergence of gapless Nambu-Goldstone modes due to spontaneously broken continuous phase and translation symmetries. For the recent implementation of the polariton nonequilibrium supersolidity in semiconductor metasurfaces [D. Trypogeorgos et al., Nature 639, 337 (2025)], we demonstrate the key role of attractive polariton interactions, mediated by the excitonic reservoir, for stability of the supersolid phase. Performing a thorough numerical investigation, we identify the conditions for existence of the diagonal and off-diagonal long-range order in negative-mass nonequilibrium supersolids.