Symmetry-breaking vortex-lattice of a binary superfluid in a rotating bucket

We study spontaneous-symmetry-broken phase-separated vortex lattice in a weakly interacting uniform rapidly rotating binary Bose superfluid contained in a quasi-two-dimensional circular or square bucket. For the inter-species repulsion above a critical value, the two superfluid components separate and form a demixed phase with practically no overlap in the vortex lattices of the two components, which will permit an efficient experimental observation of such vortices and study their properties. In case of a circular bucket with equal intra-species energies of the two components, the two components separate into two non-overlapping semicircular domains for all frequencies of rotation $\Omega$ generating distinct demixed vortex lattices. In case of a binary Bose superfluid in both circular and square buckets, (a) the number of vortices increases linearly with $\Omega$ in agreement with a suggestion by Feynman, and (b) the rotational energy in the rotating frame decreases quadratically with $\Omega$ in agreement with a suggestion by Fetter.