Anisotropic Fermi Superfluid via $p$-Wave Feshbach Resonance

We investigate theoretically fermionic superfluidity induced by Feshbach resonance in the orbital $p$-wave channel and determine the general phase diagram. In contrast with superfluid ${}^3\mathrm{He}$, due to the dipole interaction, the pairing is extremely anisotropic. When this dipole interaction is relatively strong, the pairing has symmetry $k_z$. When it is relatively weak, it is of symmetry $k_z+i\beta k_y$ (up to a rotation about $\widehat{z}$, here $\beta <1$). A phase transition between these two states can occur under a change in the magnetic field or the density of the gas.

Figure 1

The dimensionless order parameter ${\tilde{D}}_0$ and chemical potential $\tilde{\mu }$ as functions of the scaled parameter $-1/{\tilde{v}}_0$ in the two-body scattering amplitude. ${\tilde{c}}_0={\tilde{c}}_1=-100$ and ${\tilde{D}}_{\pm 1}=0$ in this case. The dashed line represents $-{ϵ}_b/2{ϵ}_F$.

Figure 2

Contour plot of ${\tilde{D}}_1={\tilde{D}}_{-1}$ as a function of $-1/{\tilde{v}}_1+1/{\tilde{v}}_0$ and $-1/{\tilde{v}}_0$ for ${\tilde{c}}_0={\tilde{c}}_1=-100$. The line for ${\tilde{D}}_{\pm 1}=0$ corresponds to the critical value $-1/{\tilde{v}}_1^{*}+1/{\tilde{v}}_0$ separating two different superfluid phases.