}}(-{\bf k}),\left[-t_{\rm hole}\mathcal{T}_{\rm hole}^{(0)}({\bf R},{\bf r}_0),{\sigma^{d}_{\hat x}}({\bf k})\right]\right] &=& 0t_{\rm hole}\mathcal{T}_{\rm hole}^{(0)}({\bf R},{\bf r}_0)(0-\cos({\bf k}\cdot{\bf r}_0/0))\end{aligned}$$  