Self-bound vortex lattice in a rapidly rotating quantum droplet

A rapidly rotating Bose gas in the quantum Hall limit is usually associated with a melted vortex lattice. In this work, we report a self-bound and visible triangular vortex lattice without melting for a two-dimensional Bose-Bose droplet rotating in the quantum Hall limit, i.e., with rotation frequency $\mathrm{\Omega }$ approaching the trapping frequency $\omega$. Increasing $\mathrm{\Omega }$ with respect to interaction strength $U$, we find a smooth crossover of the vortex lattice droplet from a needling regime, as featured by small vortex cores and an equilibrium flat-top surface, to the lowest-Landau-level regime with Gaussian-extended cores spreading over the whole surface. The surface density of such a rotating droplet is higher than that of a static one, and their ratio is found to be a universal function of $\mathrm{\Omega }\mathrm{/}U$. We have demonstrated these results by both numerical and variational methods. The results pave the way for future experimental exploration of rapidly rotating ultracold droplets into the quantum Hall limit.