$MX_{2}$ (e.g. $M$=Mo,W and $X$=S,Se) consist of $X$-$M$-$X$ layers, and within each layer the $M$ atoms (or the $X$ atoms) form a 2D hexagonal lattice. Each $M$ atoms is surrounded by 6 nearest neighbor $X$ atoms in a trigonal prismatic geometry with $D_{3h}^{1}$ symmetry. The valence band maxima and conduction band minima occur at the $K$ and $K'$ points in the Brillouin zone. Most of the weight in the conduction and valence band Bloch states near the $K$ and $K'$ points resides on the d-orbitals of $M$ atoms [@Falko13; @yao12; @timothy]. The spin up and down valence bands are split near the $K$ and $K'$ points by 0.1-0.2 eV due to the spin-orbit-coupling [@Falko13; @yao12; @timothy; @Liu14]. In comparison, the spin-orbit-coupling effects in the conduction band are much smaller [@Liu14]. Assuming only d-orbitals for the conduction and valence band states, and including spin-orbit coupling, one obtains the following simple spin-dependent tight-binding Hamiltonian (in matrix form) near the $K$($K'$) points [@yao12], $$\left[
\begin{array}{cc}
\Delta/2 & \hbar v k_{-} \\
\hbar v k_{+} & -\Delta/2 + \lambda \tau \sigma
\end{array} \right]    \label{eq:H1}$$ Here, $\Delta$ is related to the material bandgap, $\sigma=\pm1$ stands for the electron spin, $\tau=\pm1$ stands for the $K$ and 