The chiral
p-wave (${p}_{x}\ifmmode\pm\else\textpm\fi{}i{p}_{y}$) superfluid has attracted significant attention in recent years, mainly because its vortex core supports a Majorana fermion which, due to its non-Abelian statistics, can be explored for implementing topological quantum computation. Mixing dipolar bosons with fermions in quasi-two-dimensional space offers the opportunity to use the roton minimum as a tool for engineering the phonon-induced attractive interaction between fermions. We study, within the Hartree-Fock-Bogoliubov approach, the
p-wave superfluid pairings in a quasi-two-dimensional dipolar Bose-Fermi mixture. We show that enhancing the induced interaction by lowering the roton minimum can affect the stability property of the mixture as well as the effective mass of the fermions in an important way. We also show that one can tune the system to operate in stable regions where chiral
p-wave superfluid pairings can be resonantly enhanced by lowering the energy cost of the phonons near the roton minimum.
The recent experimental progress in realizing Bose-Fermi mixtures and dipolar quantum gases has created the exciting possibility of creating dipolar Bose-Fermi mixtures with intriguing and unique properties. In a dipolar condensate, the dipole-dipole interaction represents a control knob inaccessible to nondipolar Bosons. Thus, mixing dipolar bosons with fermions may open up new possibilities for creating superfluids with unconventional pairings. We consider a mixture of a spin-polarized Fermi gas and a dipolar Bose-Einstein condensate in a three-dimensional setting in which s-wave scattering between fermions and the quasiparticles of the dipolar condensate can result in an effective attractive Fermi-Fermi interaction anisotropic in nature and tunable by the dipolar interaction. We develop a procedure which allows us to determine the parameters such as densities and scattering lengths that are required to achieve optimal critical temperature before the system starts to phase separate. We perform a systematic investigation, finding that a superfluid with a critical temperature, that is orders of magnitude higher than achievable in nondipolar mixtures, can be realized in dipolar mixtures at experimentally accessible densities and scattering lengths before the system phase separates.