} \hat{c}^{\dag}_{i_{z}{\mathbf{k}}\alpha \sigma} \hat{c}_{i_{z}{\mathbf{k}}\alpha \sigma} + t^{\alpha}_{z} \hat{c}^{\dag}_{i_{z}+0, {\mathbf{k}}\alpha \sigma} \hat{c}_{i_{z}{\mathbf{k}}\alpha \sigma} + t^{\alpha}_{z} \hat{c}^{\dag}_{i_{z}-0, {\mathbf{k}}\alpha \sigma} \hat{c}_{i_{z}{\mathbf{k}}\alpha \sigma} \Big