Figure 1

Phase diagram for a dipolar Fermi gas in a bilayer at fixed interlayer distance, $k_{F}d=2$, as a function of $\theta$ (see Fig. 2) and interaction $U=m{D}^2{k}_F/{\hslash }^2$. The liquid phase is superfluid (SF). The (green) open triangles [circles] set the boundary of the stripe phase oriented along $\varphi =0$ [$\varphi =\pi /2$], derived from a self-consistent STLS calculation. The filled (green) square at ${\theta }_c\simeq 0.75$ and $U\simeq 15.65$ is a quantum critical point beyond which there is a phase transition between the two stripe phases. The (blue) open diamonds for the $\varphi =0$ stripe phase are instead determined including exchange correlations only (see text). These boundaries can be compared to the $\varphi =\pi /2$ stripe transition (dashed line) and the collapse instability (dashed-dotted line) for the single-layer case.[16] The shaded “bosonic” region is where the system can be described in terms of interlayer bosonic dimers. The (red) filled diamond and thick (red) line at $\theta =\pi /2$ indicate collapse in the bilayer.Reuse & Permissions

Figure 2

Critical wave vector $q_c/k_F$ for the $\varphi =\pi /2$ stripe phase ($\theta <{\theta }_c$) and the $\varphi =0$ one ($\theta >{\theta }_c$); same parameters and symbol scheme as in Fig. 1. The insets depict the alignment of the dipoles with the electric field $\mathbf{E}$ and the features of the two different stripe phases. For the $\varphi =0$ stripe phase, the density modulations in the two layers have a phase shift $\eta \simeq 2\theta$, while the wave vector $q_c$ decreases with increasing tilt angle $\theta$ down to $q_c=0$ for $\theta =\pi /2$ (filled [red] diamond), where the gas collapses. For density modulations along $\varphi =\pi /2$, $q_c$ appears to be fixed by the density.Reuse & Permissions

Figure 3

Intra- and interlayer pair correlation functions $g_{ij}\left(\mathbf{r}\right)$ for increasing values of the interaction strength $U$ towards the $\varphi =\pi /2$ stripe phase ($\theta =0$ top panel) and the $\varphi =0$ phase ($\theta =1.1\simeq 0.35\pi$ bottom panel).Reuse & Permissions