Finite-temperature properties of attractive three-component fermionic atoms in optical lattices

We investigate the finite-temperature properties of attractive three-component (colors) fermionic atoms in optical lattices using a self-energy functional approach. As the strength of the attractive interaction increases in the low-temperature region, we observe a second-order transition from a Fermi liquid to a color superfluid (CSF), where atoms from two of the three colors form Cooper pairs. In the strong attractive region, we observe a first-order transition from a CSF to a trionic state, where three atoms with different colors form singlet bound states. A crossover between a Fermi liquid and a trionic state is observed in the high-temperature region. We present a phase diagram covering zero to finite temperatures. We demonstrate that the CSF transition temperature is enhanced by the anisotropy of the attractive interaction.

Figure 1

(Color online) (a) $\left|U\right|/t$ dependence of the CSF order parameter $\Phi$, the quasiparticle weight $Z$, and the entropy per site $S/L$. (b) The single-particle excitation spectra of the $\alpha =1$ atoms ${\rho }_1\left(\omega /t\right)$ $\left[={\rho }_2\left(\omega /t\right)\right]$ and those of the $\alpha =3$ atoms ${\rho }_3\left(\omega /t\right)$ at $U/t=-1.4$. (c) The single-particle excitation spectra $\rho \left(\omega /t\right)$ $\left[\equiv {\rho }_1\left(\omega /t\right)={\rho }_2\left(\omega /t\right)={\rho }_3\left(\omega /t\right)\right]$ at $U/t=-3.0$.

Figure 2

(Color online) (a) $\left|U\right|/t$ dependence of the CSF order parameter $\Phi$ and the entropy per site $S/L$. (b) $T/t$ dependence of $\Phi$ and $S/L$.

Figure 3

(Color online) Phase diagram of the isotropic attractive three-component Hubbard model at half filling.

Figure 4

(Color online) CSF transition temperature $T_{\text{CSF}}$ as a function of $\left|U\right|/t$ with $R=1.0$, 0.5, 0.2, and 0. The broken lines are the crossover lines for $R=1.0$, 0.5, and 0.2 from left to right.