Ordered phases in a bilayer system of dipolar fermions

The liquid-to-ordered phase transition in a bilayer system of fermions is studied within the context of our recently proposed density-functional theory [B. P. van Zyl, W. Kirkby, and W. Ferguson, Phys. Rev. A 92, 023614 (2015)]. In each two-dimensional layer, the fermions interact via a repulsive, isotropic dipolar interaction. The presence of a second layer introduces an attractive interlayer interaction, thereby allowing the presence of inhomogeneous density phases which would otherwise be energetically unfavorable. For any fixed layer separation, we find an instability to a commensurate one-dimensional stripe phase in each layer, which always precedes the formation of a triangular Wigner crystal. However, at a certain fixed coupling, tuning the separation can lead to the system favoring a commensurate triangular Wigner crystal, or one-dimensional stripe phase, completely bypassing the Fermi liquid state. While other crystalline symmetries, with energies lower than the liquid phase can be found, they are never allowed to form owing to their high energetic cost relative to the triangular Wigner crystal and stripe phase.

Figure 1

Phase diagram of the bilayer system. As discussed in the text, ${\lambda }_0$ is the dimensionless coupling and $r_0$ is the dipolar length scale. For $\tilde{\gamma }=\gamma /r_0\gtrsim 4$, the two layers are effectively uncoupled, and we reproduce the results found in Ref. [1]. The solid curve delineates the boundary between the liquid and 1DSP, while the solid curve with triangles separates the 1DSP from the TWC. The liquid $\to 1\text{DSP}$ and 1DSP $\to$ TWC are first-order phase transitions. Inset: A schematic depiction of the model under consideration. In each 2D layer, the atoms have their dipole moments (represented by the arrows) aligned with the $z$ axis. The layers are separated by a distance $\gamma$.