  = \sum_{\mathbf{k}} (-a_{\mathbf{k}}^{\dagger } a_{\mathbf{k}} + b_{\mathbf{k}}^{\dagger } b_{\mathbf{k}}) = \sum_{\mathbf{k}}(-{\cal{A}}_{\mathbf{k}}^{\dagger } {\cal{A}}_{\mathbf{k}} + {\cal{B}}_{\mathbf{k}}^{\dagger } {\cal{B}}_{\mathbf{k}}) $