reflection about the Fe plane, we may define a pseudocrystal momentum $\bf{\tilde{k}}$ in the extended one-Fe BZ. This pseudocrystal momentum and the conventional momentum $\bf{k}$ are related by $\bf{\tilde{k}}=\bf{k}+\bf{Q}$ in [$d_{xz}$]{} and [$d_{yz}$]{} orbitals (where $\bf{Q}=(\pi,\pi)$), but $\bf{\tilde{k}}=\bf{k}$ in other orbitals. In the extended BZ, the tight-binding Hamiltonian reads

$$\label{eqn:eqn2}
H_{\mathrm{kin}}=\sum\limits_{\bf{\tilde k}\alpha\beta\sigma}[\xi_{\alpha\beta}(\bf{\tilde k})+(\Delta_\alpha-\mu)\delta_{\alpha\beta}]d^{\dagger}_{\bf{\tilde k}\alpha\sigma}d_{\bf{\tilde k}\beta\sigma}.$$

Here $\xi_{\alpha\beta}(\bf{\tilde{k}})$ is the hopping matrix in the momentum space associated with orbitals $\alpha$ and $\beta$, $\Delta_{\alpha}$ is the on-site energy reflecting the crystal field splitting, $\mu$ is the chemical potential, and $\delta_{\alpha\beta}$ is the Kronecker’s delta function. The expression of $\xi_{\alpha\beta}(\bf{\tilde{k}})$ is given in Ref. [@s7yu], and it has the same form as appeared in the appendix of Ref. [@s2graser]. We adopt the tight-binding parameters of Ref. [@s7yu], where they are obtained by fitting the LDA band structure of KFS. To better fit the LDA results, we have further tuned several hopping parameters by hand from their values in Ref. [@s7yu]. Using the same notation as in Ref. [@s2graser], the tight-binding parameters used in this paper for KFS are listed in Table \[Table:tab1\]. The chemical potential corresponding to the electron filling $n$=6.15 is $\mu$=-0.365 eV.

The five-orbital Hubbard model is studied using the recently 