Competing many-body instabilities in two-dimensional dipolar Fermi gases

Experiments on quantum degenerate Fermi gases of magnetic atoms and dipolar molecules begin to probe their broken-symmetry phases dominated by the long-range, anisotropic dipole-dipole interaction. Several candidate phases including the $p$-wave superfluid, the stripe density wave, and a supersolid have been proposed theoretically for two-dimensional spinless dipolar Fermi gases. Yet the phase boundaries predicted by different approximations vary greatly and a definitive phase diagram is still lacking. Here we present a theory that treats all competing many-body instabilities in the particle-particle and particle-hole channel on equal footing. We obtain the low-temperature phase diagram by numerically solving the functional renormalization-group flow equations and find a nontrivial density wave phase at small dipolar tilting angles and strong interactions, but no evidence of the supersolid phase. We also estimate the critical temperatures of the ordered phases.

Figure 1

(a) The phase diagram of two-dimensional spinless dipolar Fermi gas at $T=0.01E_F$ predicted by FRG. It displays a Fermi liquid (FL), a $p$-wave superfluid (BCS), and two distinct density wave phases, ${\mathrm{DW}}_1$ and ${\mathrm{DW}}_2$. The color map shows the critical scale ${\mathrm{\Lambda }}_c$ at which the vertex diverges (see the main text). Three representative points ${\mathcal{P}}_1,{\mathcal{P}}_2$, and ${\mathcal{P}}_3$ on the phase diagram are chosen to show the details of the FRG flow. (b) The flows of the largest eigenvalue of $V_{\mathrm{BCS}}$ and the two largest eigenvalues of $V_{\mathrm{DW}}$ corresponding to the ${\mathrm{DW}}_1$ and ${\mathrm{DW}}_2$ order, respectively. (c) The eigenvectors of the leading instability and the corresponding channel matrices near the end of the flow.

Figure 2

The critical temperature $T_c$ as a function of the dipole tilting angle $\theta$ for fixed interaction $g=1.5$ estimated from the FRG flow. Dashed lines are the extensions of the fits to the data points in the ${\mathrm{DW}}_1$ and ${\mathrm{DW}}_2$ region, respectively.