$K'$ valleys, $2\lambda$ is the splitting of the valence band due to spin-orbit coupling, $k_{\pm}=\tau k_{x}\pm ik_{y}$, and the velocity parameter $v$ is related to the coupling between the orbitals on neighboring $M$ atoms. From density functional theories [@Lam12; @Falko13], $v\approx 5-6 \times 10^5 $ m/s. The wavevectors are measured from the $K$($K'$) points. The d-orbital basis used in writing the above Hamiltonian are $| d_{z^{2}} \rangle$ and $(| d_{x^{2}-y^{2}}\rangle + i\tau | d_{xy}\rangle)/\sqrt{2}$ [@yao12]. We will use the symbol $s$ for the combined valley ($\tau$) and spin ($\sigma$) degrees of freedom. Defining $\Delta_{s}$ as $\Delta - \lambda \tau \sigma$, the energies and eigenvectors of the conduction and valence bands are [@yao12; @Efimkin13], $$E_{{c \atop v},s}(\vec{k}) = \frac{\lambda \tau \sigma}{2} + \gamma \sqrt{ (\Delta_{s}/2)^{2} + (\hbar v k)^{2}}$$ $$| v_{{c \atop v},\vec{k},s}\rangle  = \left[ \begin{array}{c} \cos(\theta_{\gamma,\vec{k},s}/2) e^{-i\tau\phi_{\vec{k}}/2} \\ \tau \gamma \sin(\theta_{\gamma,\vec{k},s}/2) e^{i\tau\phi_{\vec{k}}/2} \end{array} \right] \label{eq:wf1}$$ Here, $\gamma =1$ (or $-1$) stands for the conduction (or the valence) band, $\phi_{\vec{k}}$ is the phase of the wavevector $\vec{k}$, and, $$\cos(\theta_{\gamma,\vec{k},s}) = \gamma \frac{\Delta_{s}}{2 \sqrt{ (\Delta_{s}/2)^{2} + (\hbar v k)^{2}}} \label{eq:cs}$$ Near the conduction band minima and valence band maxima, the band energy dispersion is parabolic with well-defined effective masses, $m_{e}$ and $m_{h}$, 