their real spins. In this work, we show in the following sections that the MF potential can be readily extended to incorporate these additional degrees of freedom (DoF) which we shall for simplicity refer to collectively as pseudospin. To first order in the electric field, the MF potential accounts for the effects of a constant, in-plane electric field for the purposes of calculating spin / charge currents and spin accumulations to first order in the electric field.

We illustrate the application of the MF potential on a system with a spin$\otimes$pseudospin degrees of freedom through the example of the topological insulator (TI) thin film system [@PRB80_205401; @PRB81_041307; @PRB81_115407]. Unlike a semi-infinite TI slab, a TI thin film has both a top and a bottom surface which, due t the finite thickness, couple to each other. The low energy effective Hamiltonian for can be written as $$H = v(\vec{k}\times\vec{\sigma})\cdot\hat{z} \tau_z + \lambda \tau_x + \vec{M}\cdot\vec{\sigma} \label{TIham1}$$ Besides the real spin denoted as $\vec{\sigma}$ of the charge carriers there is another discrete degree of freedom $\vec{\tau}$ associated with whether the charge carriers are localized nearer the upper ( $|+\tau_z\rangle\langle +\tau_z|$ ) or lower ($|-\tau z \rangle\langle -\tau_z|$) surface of the film. The 