Vortex-lattice structures in rotating Bose-Fermi superfluid mixtures

The system of Bose-Fermi superfluid mixture offers a playground to explore rich macroscopic quantum phenomena. In a recent experiment of Yao {\it et al.} [Phys. Rev. Lett. {\bf 117}, 145301 (2016)], $^{41}$K-$^{6}$Li superfluid mixture is implemented. Coupled quantized vortices are generated via rotating the superfluid mixture, and a few unconventional behaviors on the formations of vortex numbers are observed, which can be traced to boson-fermion interactions. Here we provide a theoretical insight into the unconventional behaviors observed in the experiment. To this end, the orbital-free density functional theory is hired, and its utility is validated by making comparison of the numerical results and a microscopic theory for vortex lattices in strongly interacting Fermi superfluids alone. We also predict interesting phenomena which can be readily explored experimentally, including the novel structures of bosonic-fermionic vortices, and attractive interactions between the bosonic and fermionic vortices.