Unitary Fermi Supersolid: The Larkin-Ovchinnikov Phase

We present strong theoretical evidence that a Larkin-Ovchinnikov (LOFF/FFLO) pairing phase is favored over the homogeneous superfluid and normal phases in three-dimensional unitary Fermi systems. Using a density functional theory (DFT) based on the latest quantum Monte Carlo calculations and experimental results, we show that this phase is competitive over a large region of the phase diagram. The oscillations in the number densities and pairing field have a substantial amplitude, and a period some 3 to 10 times the average interparticle separation. Within the DFT, the transition to a normal polarized Fermi liquid at large polarizations is smooth, while the transition to a fully paired superfluid is abrupt.

Figure 1

The dimensionless convex function $g(x)$ [25] that defines the energy density $\mathcal{E}(n_a,n_b)=\frac{3}{5}\frac{{\hslash }^2}{2m}(6{\pi }^2{)}^{2/3}[n_{a}g(x){]}^{5/3}$. The points with error-bars (blue) are the Monte Carlo data from Ref. 20. The fully paired solution $g(1)=(2\xi {)}^{3/5}$ is indicated to the bottom right, and the recent MIT data [26] are shown (light $\times$) for comparison. The phase separation discussed in Ref. [20] is shown by the Maxwell construction (thin black dashed line) of the 1st-order transition $y=y_{N\mathrm{\text{−}}\mathrm{SF}}$ in Fig. 2. The LO state (thick red curve) has lower energy than all pure states and phase separations previously discussed. The Maxwell construction of the weakly 1st-order transition $y=y_{\mathrm{LO}\mathrm{\text{−}}\mathrm{SF}}$ in Fig. 2 is shown by the thick dashed line (red).

Figure 2

The dimensionless convex function $h(y)$ [25] that defines the average pressure $\mathcal{P}({\mu }_a,{\mu }_b)=\frac{2}{5}(\frac{2m}{{\hslash }^2}{)}^{3/2}[{\mu }_{a}h(y){]}^{5/2}/(6{\pi }^2)$ is constrained to the thin dotted triangular region [25]. The interacting normal state pressure [20] defining our ASLDA functional constrains this further (thin blue line), and displays a 1st-order transition at $y_{N\mathrm{\text{−}}\mathrm{SF}}$ where normal and SF phases could coexists (Maxwell construction in Fig. 1). The LO state has an even higher pressure (thick red line), replacing much of this region, including the former $y_{N\mathrm{\text{−}}\mathrm{SF}}$ transition. The $y$ dependence of the amplitude of the pairing field $\Delta =\max \{|\Delta (z)|\}$ and the period $L$ are shown inset. Sample profiles for the states marked $\times$ are shown in Fig. 3. Units are fixed in terms of ${\mu }_{-}=({\mu }_a-{\mu }_b)/2$ [28].

Figure 3

A single LO period showing the spatial dependence of the pairing field $\Delta (z)$ (top) and the number densities of the majority (dotted) and minority (solid) species (bottom) at the values of $y\in (y_{\mathrm{LO}\mathrm{\text{−}}N},y_{\mathrm{LO}\mathrm{\text{−}}\mathrm{SF}})$ marked by $\times$ in Fig. 2. Units are fixed in terms of ${\mu }_{-}$ [28].