Emergent interlayer nodal superfluidity of a dipolar Fermi gas in bilayer optical lattices

Understanding the interplay between magnetism and superconductivity is one of the central issues in high-temperature superconductors. The recent experimental implementation of cold gases with highly tunable anisotropic interaction, especially in magnetic dipolar atoms or polar molecules, opens up a new thrust on exploring this interesting phenomenon. Here we report a mechanism to drive the interplay between magnetism and superfluidity through engineering the spatially anisotropic interaction via considering loading pseudospin-1/2 dipolar Fermi atoms in bilayer optical lattices. Surprisingly, we find that the weak interlayer interaction can lead to the coexistence of superfluidity and antiferromagnetism at low temperatures for the half filling case. It is distinguished from the usual scheme by doping an antiferromagnetic Mott insulating parent to access high-$T_c$ superconductivity, where at half filling there is no coexistence of superconductivity and magnetism at low temperatures due to the absence of the superconductivity. Furthermore, the interlayer superfluid possesses an unexpected nodal structure, which is reminiscent of the nodal high-$T_c$ superconductivity but differs in origin.

Figure 1

Schematic picture of the bilayer optical lattice system. Within each single layer, there is a gas of interacting pseudospin-$1/2$ dipolar Fermi atoms loaded in the same 2D square optical lattice with the lattice constant $a$. Here the red and yellow balls attached with up and down arrows stand for the pseudospin up and down fermionic dipolar atoms, respectively. By assuming an external magnetic (electric) field applied, all the magnetic (electric) dipole moments are aligned along the same direction, which is perpendicular to the layers (the dipole moment is not shown in the figure). $\lambda$ is the interlayer distance. To treat with the intralayer antiferromagnetism, we decompose the square optical lattice within each single layer into two sublattices $A$ and $B$, where the pseudospins are aligned oppositely between $A$ and $B$ site.

Figure 2

(a) Zero-temperature phase diagram as a function of the interlayer distance $\frac{\lambda }{a}$ and interlayer interaction strength $D=\frac{d^2}{t{a}^3}$ with a fixed intralayer interaction strength $\frac{g}{t}=20$ when considering a half-filling case. (b) The Berezinskii-Kosterlitz-Thouless (BKT) transition temperature of the interlayer superfluids as a function of the interlayer distance when considering interlayer interaction strength $D=1.25$ and other parameters are the same as in (a).

Figure 3

(a) Nodal gap structure of interlayer superfluid (showing the amplitude of superfluid gap ${\mathrm{\Delta }}_{\uparrow \uparrow }$ here). (b) The amplitude of structure function (defined in the main text) $S_{\uparrow \uparrow }$. (c) The interlayer interaction $\frac{V_{\mathbf{q}}}{t}$ [defined in Eq. (6)] in the momentum space. Here the interlayer distance $\frac{\lambda }{a}=1$, interlayer interaction strength $D=3$, and other parameters are the same as in Fig. 2.