The minimum model for the iron-based superconductors

A single band $t$-$U$-$J_1$-$J_2$ model is proposed as the minimum model to describe the superconductivity of the newly discovered iron-based superconductors $R(O_{1-x}{F}_x)FeAs$ and $R{O}_{1-x}FeAs$ ($R=La, Ce, Sm, Pr, Nd,Gd$). With the mean-field approach, it is found that the pairing occurs in the d-wave channel. In the likely parameter region of the real materials, by lowering temperature, the system enters firstly the $d_{xy}$ superconducting phase with $D_{4h}$-symmetry and then enters the time-reversal-symmetry-broken $d_{xy}+i{d}_{x^2-y^2}$ superconducting phase with $C_{4h}$-symmetry.