Supersolid Phase with Cold Polar Molecules on a Triangular Lattice

We study a system of heteronuclear molecules on a triangular lattice and analyze the potential of this system for the experimental realization of a supersolid phase. The ground state phase diagram contains superfluid, solid, and supersolid phases. At finite temperatures and strong interactions there is an additional emulsion region, in contrast with similar models with short-range interactions. We derive the maximal critical temperature $T_c$ and the corresponding entropy $S/N=0.04(1)$ for supersolidity and find feasible experimental conditions for its realization.

Figure 1

Ground state phase diagram for the Hamiltionian equation (1) around a filling factor $n=\frac{1}{3}$ with $t$ the tunneling amplitude and $V$ the interaction strength. The phases are a superfluid “SF”, supersolid “SS”, and a commensurate solid at filling factor $n=\frac{1}{3}$. With the double line we indicate a transition region of the Spivak-Kivelson bubble type (emulsions) gradually going over to a region of incommensurate, floating solids with increasing interaction strength. For large interaction strength, and starting around half filling, the supersolid phase is suppressed by emerging solid ordering (stripes at half filling and incommensurate, floating solids at other fillings).

Figure 2

Density $n$, superfluid density ${\rho }_s$, and structure factor $S_{\overrightarrow{Q}}/L^2$ for $V/t=15$ as a function of chemical potential $\mu$. Statistical errors are smaller than symbol sizes if not shown.

Figure 3

Superfluid density ${\rho }_s$ and structure factor $S_{\overrightarrow{Q}}/L^2$ as a function of temperature $T/t$ at fixed filling factor $n=0.4$ and interaction strength $V/t=12$. At low temperatures we have a supersolid phase with both commensurate, solid order and a finite superfluid density. Although small system sizes show a continuous transition reminiscent of a two-dimensional 3-state Potts transition, a careful analysis reveals nonmonotonicity and hysteresis in the structure factor for larger system sizes, which is the first evidence for more complex physics in the emulsion phase.

Figure 4

Finite temperature phase diagram at fixed filling factor $n=0.4$. The superfluid to normal liquid and the superfluid to supersolid transitions are found to be continuous (see text). After the Kosterlitz-Thouless (KT) and two-dimensional 3-state Potts transition lines cross, an intermediate phase of emulsions appears between the normal and the supersolid phases. The hatched region denotes where we found such emulsions for $L=24$.