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Vorticity-Crystalline Order Coupling in Supersolids: Excitations and Re-entrant Phases

Rotation is a natural tool in ultracold gases to break time-reversal symmetry, yet its impact on the collective excitations of supersolids remains largely unexplored. We show theoretically that tuning the rotation frequency, rather than the interparticle interactions, can trigger the superfluid-to-supersolid transition in Bose-Einstein condensates (dBECs). Computing excitation spectra in the presence of vortices and persistent currents, we uncover a vortex-driven de-softening mechanism whereby quantized vorticity elevates the gapless Goldstone mode to a finite-energy roton, restoring superfluidity. This effect results in re-entrant supersolid phases as a function of rotation frequency, revealing a fundamental coupling between topological defects and crystalline order.