Supersolid versus Phase Separation in Atomic Bose-Fermi Mixtures

We show that a two-dimensional atomic mixture of bosons and fermions cooled into their quantum degenerate states and subject to an optical lattice develops a supersolid phase characterized by the simultaneous presence of a nontrivial crystalline order and phase order. This transition is in competition with phase separation. We determine the phase diagram of the system and propose an experiment allowing for the observation of the supersolid phase.

Figure 1

Left: sketch of the ${\lambda }_{\mathrm{F}\mathrm{B}}\mathrm{\text{−}}1/t_{\mathrm{B}}\mathrm{\text{−}}T$ phase diagram. For $T_{\mathrm{D}\mathrm{W}}>T_{\mathrm{P}\mathrm{S}}$ the low temperature phase at $T<T_{\mathrm{D}\mathrm{W}}$ is a supersolid (SS), while phase separation (PS) emerges at $T<T_{\mathrm{P}\mathrm{S}}$ for $T_{\mathrm{P}\mathrm{S}}>T_{\mathrm{D}\mathrm{W}}$. Right: bosonic density $n_{\mathrm{B}}(x,y)$ for the superfluid (SF), phase separated, and supersolid phases.

Figure 2

Left: first Brillouin zone $K$ and Fermi surface of 2D fermions in an optical lattice. The solid lines denote the Fermi surface at half filling. Right: density of states with logarithmic Van Hove singularities $N(ϵ)\sim N_0\ln |16J_{\mathrm{F}}/ϵ|$.

Figure 3

Left: $V_{\mathrm{F}}\mathrm{\text{−}}\gamma$ phase diagram at low temperatures. Increasing the strength of the optical lattice in an experiment allows us to drive the supersolid into phase separation. Right: transition temperatures for $\gamma =3$ ($E_{\mathrm{F}}^r=347\mathrm{n}\mathrm{K}$).