$F$-wave pairing of cold atoms in optical lattices

The tremendous development of cold atom physics has opened up a whole new opportunity to study novel states of matter which are not easily accessible in solid-state systems. Here we propose to realize the $f$-wave pairing superfluidity of spinless fermions in $p_{x,y}$-orbital bands of two-dimensional honeycomb optical lattices. The nontrivial orbital band structure, rather than strong correlation effects, gives rise to the unconventional pairing with the nodal lines of the $f$-wave symmetry. With a confining harmonic trap, zero-energy Andreev bound states appear around the circular boundary with a sixfold symmetry. The experimental realization and detection of this novel pairing state are feasible.

Figure 1

Orbital configurations of the lower dispersive band 2 at high-symmetry points and lines in the BZ. The time-reversal partners ${\psi }_2(\pm \mathrm{k⃗})$ involve the same polar orbital only if $\mathrm{k⃗}$ is along the three middle lines and take the complex orthogonal orbitals of $p_x\pm {\mathit{ip}}_y$ with opposite chiralities at $\mathrm{K⃗}$ and ${\mathrm{K⃗}}^{\prime }$. $\omega =e^{i\frac{\pi }{6}}$.

Figure 2

(a) The $f$-wave pairing form factor $F(\mathrm{k⃗})$ for intraband pairing in momentum space. (b) The $f$-wave pairing pattern in real space with ${\Delta }_A=-{\Delta }_B=\Delta$.

Figure 3

Gap and superfluid density for the $f$-wave state at $U/t_{\parallel }=2.2$ and $0.7<n<1.0$. (a) The pairing amplitude ${\Delta }_A=-{\Delta }_B=\Delta$ until $n\approx 0.9$. For $n>0.9$, the CDW order starts to coexist with the $f$-wave pairing superfluid, resulting in an $f$-wave supersolid state. (b, c) Lowest-energy branch of Bogoliubov excitations at $n=0.89$ and $n=0.78$. For a better visual effect, only negative eigenvalues are shown. (d) Superfluid density ${\rho }_s$ vs. $n$.

Figure 4

(a) Zero-energy Andreev bound states appear on the boundary perpendicular to the antinodal directions. (b) The zero-energy $L_{\mathrm{DOS}}$ in real space with the maximal value at $\theta =n\pi /3$ is a signature of the $f$-wave pairing symmetry.

Figure 5

$F[y(l_z/l)]$ as a function of $l_z/l$.