Metanematic, smectic, and crystalline phases of dipolar fermions in an optical lattice

It has been suggested that some strongly correlated matter might be understood qualitatively in terms of liquid crystalline phases intervening between the Fermi gas and the Wigner crystal or Mott insulator. We propose a tunable realization of this soft quantum matter physics in an ultracold gas. It uses optical lattices and dipolar interactions to realize a particularly simple model. Our analysis reveals a rich phase diagram featuring a metanematic transition where the Fermi liquid changes dimensionality; a smectic phase (stripes) and a crystalline “checkerboard” phase.

Figure 1

(Color online) Right: proposed experimental setup. Dipolar atoms or molecules (1–6) are loaded on a 2D anisotropic optical lattice in a strong external magnetic or electric field (B). The field is oriented so that all interactions between lattice sites are repulsive and there are no intrachain interactions (see text). Left: interaction potential in reciprocal space for three values of the anisotropy parameter $\alpha =0.5$ (top), 1.0, and 2.0 (bottom).

Figure 2

(Color online) Dependence of the renormalized transverse hopping $t_{\perp }^{\ast }$ on its bare value $t_{\perp }$ for $V=3t_{\parallel }$ and $\mu =-1.5t_{\parallel }$. The solid (dashed) lines correspond to solutions to the self-consistency equation (2) that minimize (maximize) the energy. Insets: Fermi surface (a) just to the left of the bifurcation region and (b) just to the right, as indicated, and (c) dependence of the solutions on $V$ for $t_{\perp }=0$ (rightmost curve), $0.05t_{\parallel }$, and $0.1t_{\parallel }$ (leftmost curve).

Figure 3

(Color online) (a) Phase diagram of the Hamiltonian of Eq. (1) for $\mu =\pm 1.9t_{\parallel }$. The circles track the two bifurcation points [(a) and (b) in Fig. 2] of the first-order metanematic quantum phase transition between the quasi-1D and 2D phases. The solid line marks the line of quantum critical points separating these Fermi-liquid states from the crystalline state (C). (b) Critical value of the lattice anisotropy $a_{\parallel }/a_{\perp }$ for the dominant instability to be toward the crystalline (C) or smectic (S) phases as a function of the relative strength of the renormalized perpendicular hopping $t_{\perp }^{\ast }$ for ${\mu }^{\ast }=\pm 1.9t_{\parallel }$.