Supersolid state in fermionic optical lattice systems

We study ultracold fermionic atoms trapped in an optical lattice with harmonic confinement by combining the real-space dynamical mean-field theory with a two-site impurity solver. By calculating the local particle density and the pair potential in the systems with different clusters, we discuss the stability of a supersolid state, where an $s$-wave superfluid coexists with a density-wave state of checkerboard pattern. It is clarified that a confining potential plays an essential role in stabilizing the supersolid state. The phase diagrams are obtained for several effective particle densities.

Figure 1

(Color online) Density profile $⟨n_{i\sigma }⟩$ in the optical lattice system with $d∕a=10$ at $T∕t=0.05$ when $U∕t=0.0$, 2.0, 3.0, 5.0, 7.0, and 10.0 (from top to bottom).

Figure 2

(Color online) Pair potential ${\Delta }_i$ in the optical lattice system with $d∕a=10$ at $T∕t=0.05$ when $U∕t=0.0$, 2.0, 3.0, 5.0, 7.0, and 10.0 (from top to bottom).

Figure 3

(Color online) Profiles of particle density $⟨n_{i\sigma }⟩$ and pair potential ${\Delta }_i$ as functions of $r∕d$ with fixed $d=12.5$, 17.5, and 22.5, when $U∕t=5$.

Figure 4

(Color online) $⟨n_{\pi \pi }⟩∕⟨n_{00}⟩$ and ${\Delta }_{00}∕5⟨n_{00}⟩$ as a function of the effective particle density $\tilde{\rho }(=N∕\pi d^2)$ when $U=5t$ and $T=0.05t$. The broken line represents the local particle density at the center of the lattice in the noninteracting case.

Figure 5

(Color online) Phase diagram of the attractive Hubbard model on the optical lattice with $\tilde{\rho }\sim 0.63$, 2.3, and 8.9. The density plot represents the profiles of the $s$-wave pair potential as a function of the attractive interaction $U∕t$. The DW state is realized in the shaded area. The broken lines give a guide to the eye which distinguishes the region with a fractional particle density from the empty and fully occupied regions.