Weyl Superfluidity in a Three-Dimensional Dipolar Fermi Gas

Weyl superconductivity or superfluidity, a fascinating topological state of matter, features novel phenomena such as emergent Weyl fermionic excitations and anomalies. Here we report that an anisotropic Weyl superfluid state can arise as a low temperature stable phase in a 3D dipolar Fermi gas. A crucial ingredient of our model is a direction-dependent two-body effective attraction generated by a rotating external field. Experimental signatures are predicted for cold gases in radio-frequency spectroscopy. The finite temperature phase diagram of this system is studied and the transition temperature of the Weyl superfluidity is found to be within the experimental scope for atomic dipolar Fermi gases.

Figure 1

(a) Gapless points along the $k_z$ axis, where the unit of momentum is the Fermi momentum $k_F$. (b) Illustration of the Skyrmion configuration formed by the $\overrightarrow{d}(\mathbf{k})$ vector in the ($k_x$, $k_y$) plane, with fixed $k_z\in (k_{-}^C,k_{+}^C)$. The arrows show $d_{x,y}$ components, and the colors index the $d_z$ component.

Figure 2

(a) Density of states which has been defined in the main text in units of $n_F/E_F$, where $n_F=k_F^3/6{\pi }^2$ and $E_F={\hslash }^2{k}_F^2/2m$. (b) Quasiparticle dispersion around the gapless points. There are four branches of conic energy spectra shown here. For the two branches in the middle we choose $\tilde{\theta }=\pi /10$, while for the other two we choose $\pi /2$. (c) and (d) Hedgehoglike topological defects formed by the $\overrightarrow{d}(\mathbf{k})$ vector around two Weyl nodes.

Figure 3

Anisotropic superconducting pairing order parameter with different interaction strengths $J=3$ and 7 ($J\equiv |(m{d}^{\prime 2}/{\hslash }^2)k_F|$). (a) The superconducting gap ${\mathrm{\Delta }}_F({\theta }_{\mathbf{k}})$ on the Fermi surface versus the angle ${\theta }_{\mathbf{k}}$ between the momentum $\mathbf{k}$ and $z$ axis. (b) The superconducting gap $\mathrm{\Delta }(k_{\rho },k_z)$ as a function of $k_{\rho }$ with fixed $k_z$.

Figure 4

Chemical potential $\mu$ versus the density $n$. In (a), the temperature is $T=0$, while in (b) the temperature is $k_{B}T=0.1E_F$. Here, the unit of $\mu$ is $E_d\equiv {\hslash }^6/(m^3{d}^4)$ and the unit of $n$ is $n_d\equiv [{\hslash }^2/(m{d}^2){]}^3$.

Figure 5

Finite temperature phase diagram. The solid line stands for the BCS transition temperature which separates the region between the superfluid state (SF) and normal state (NG). The area on the right-hand side of the dashed line demonstrates the instability of the system due to the strongly attractive interaction.