Superfluidity and Dimerization in a Multilayered System of Fermionic Polar Molecules

We consider a layered system of fermionic molecules with permanent dipole moments aligned perpendicular to the layers by an external field. The dipole interactions between fermions in adjacent layers are attractive and induce interlayer pairing. Because of the competition for pairing among adjacent layers, the mean-field ground state of the layered system is a dimerized superfluid, with pairing only between every other layer. We construct an effective Ising-$XY$ lattice model that describes the interplay between dimerization and superfluid phase fluctuations. In addition to the dimerized superfluid ground state, and high-temperature normal state, at intermediate temperature, we find an unusual dimerized “pseudogap” state with only short-range phase coherence. We propose light-scattering experiments to detect dimerization.

Figure 1

Schematic representation of the competition for pairing among adjacent pairs of layers, including the depiction of the optical confinement beam which creates the stack of 2D sheets (left diagram) and the illustration of one of the two equivalent dimerized pairing ground states for a many-layered system (right diagram). The wavy lines illustrate the proposed light-scattering detection scheme discussed below in the text.

Figure 2

Schematic depiction of the fully dimerized phase (a), in-plane Ising DW (b), the $z$-axis Ising DW with pairing between two adjacent pairs of layers (c), and the $z$-axis Ising DW with no pairing for two adjacent pairs of layers (d). Green shading between layers indicates pairing.

Figure 3

The lattice-model phase diagram, calculated using the temperature dependence of the GL coefficients in (3) and plotted in terms of the dipole-interaction strength $D^2/d^3$ and temperature $T$, each measured in units of ${\epsilon }_F$ (main figure). The inset shows the phase diagram predicted by the effective lattice model for generic model parameters, with $K_z/K_{\perp }=2$. The double line indicates the first-order transition.