Figure 6

The optical selection rules in pristine SL WS\(_2\) satisfy the equation \(\Delta m=\pm 1\pm 3\) for \(\sigma ^\pm\) transitions and \(\Delta m=0\pm 3\) for \(\pi\) transitions. The term \(\pm 3\) is due to the \(C_3\) rotational symmetry of the lattice. These selection rules corroborate the difference between the in-plane and out-of-plane band gaps \(E_{g||}\) and \(E_{g\perp }\), respectively. The Bloch states at the K and K’ points transform according to the IRs of the \(C_{3h}\) point group. The coefficients of the main contributions are given by \(\left| \alpha _{2,\pm 2}^\text{VB}\right| ^2=0.75\), \(\left| \beta _{1,\pm 1}^\text{VB}\right| ^2=0.25\), \(\left| \alpha _{2,0}^\text{CB}\right| ^2=0.75\), \(\left| \beta _{1,\pm 1}^\text{CB}\right| ^2=0.19\), \(\left| \alpha _{2,\pm 1}^\text{CB+1}\right| ^2=0.56\), \(\left| \beta _{1,\pm 1}^\text{CB+1}\right| ^2=0.29\).