## Appendix A On-Site and Hopping Matrices of the 6 \(\times\) 6 Block  
For convenience, we reproduce in this appendix the analytical expressions for the model. The on-site terms of the Hamiltonian can be written in the compact form [48]:  
\[\mathbf{e} = \left( \begin{array}{cc}\epsilon_{M}&0\\ 0&\epsilon_{X}\end{array} \right), \tag{10}\]  
where  
\[\epsilon_{M} = \begin{pmatrix}\Delta_{0}&0&0\\ 0&\Delta_{2}&-i\lambda_{M}\delta_{z}\\ 0&i\lambda_{M}\delta_{z}&\Delta_{2}\end{pmatrix} , \tag{11}\] \[\epsilon_{X} = \begin{pmatrix}\Delta_{p}+t_{xx}^{\perp}&-i\frac{\lambda_{X}}{2 }\delta_{z}&0\\ i\frac{\lambda_{X}}{2}\delta_{z}&\Delta_{p}+t_{yy}^{\perp}&0\\ 0&0&\Delta_{z}-t_{zz}^{\perp}\end{pmatrix} ,\]  
where \(\lambda_{M}\) and \(\lambda_{X}\) are the SOC of the metal (\(M\)) and chalcogen atoms (\(X\)), respectively, and \(\delta_{z}=\pm\) is the \(z\)-component of the spin degree of freedom [48]. The effects of vertical hopping \(V_{pp}\) between top and bottom \(X\) atoms are considered through the terms \(t_{xx}^{\perp}=t_{yy}^{\perp}=V_{pp\pi}\), and \(t_{zz}^{\perp}=V_{pp\sigma}\). The nearest-neighbor hopping between \(M\) and \(X\) atoms are  
\[t_{1}^{MX}=\frac{\sqrt{2}}{7\sqrt{7}} \begin{pmatrix}-9V_{pd\pi}+\sqrt{3}V_{pd \sigma}&3\sqrt{3}V_{pd\pi}-V_{pd\sigma}&12V_{pd\pi}+\sqrt{3}V_{pd\sigma}\\ 5\sqrt{3}V_{pd\pi}+3V_{pd\sigma}&9V_{pd\pi}-\sqrt{3}V_{pd\sigma}&-2\sqrt{3}V_ {pd\pi}+3V_{pd\sigma}\\ -V_{pd\pi}-3\sqrt{3}V_{pd\sigma}&5\sqrt{3}V_{pd\pi}+3V_{pd\sigma}&6V_{pd\pi}- 3\sqrt{3}V_{pd\sigma}\end{pmatrix} , \tag{12}\]  
\[t_{2}^{MX}=\frac{\sqrt{2}}{7\sqrt{7}} \begin{pmatrix}0&-6\sqrt{3}V_{pd\pi}+2V_ {pd\sigma}&12V_{pd\pi}+\sqrt{3}V_{pd\sigma}\\ 0&-6V_{pd\pi}-4\sqrt{3}V_{pd\sigma}&4\sqrt{3}V_{pd\pi}-6V_{pd\sigma}\\ 14V_{pd\pi}&0&0\end{pmatrix} , \tag{13}\]\[t_{3}^{MX}=\frac{\sqrt{2}}{7\sqrt{7}} \begin{pmatrix}9V_{pd\pi}-\sqrt{3}V_{pd\sigma}& 3\sqrt{3}V_{pd\pi}-V_{pd\sigma}&12V_{pd\pi}+\sqrt{3}V_{pd\sigma}\\ -5\sqrt{3}V_{pd\pi}-3V_{pd\sigma}&9V_{pd\pi}-\sqrt{3}V_{pd\sigma}&-2\sqrt{3}V_ {pd\pi}+3V_{pd\sigma}\\ -V_{pd\pi}-3\sqrt{3}V_{pd\sigma}&-5\sqrt{3}V_{pd\pi}-3V_{pd\sigma}&-6V_{pd\pi }+3\sqrt{3}V_{pd\sigma}\end{pmatrix} , \tag{10}\]  
where the direction of the hopping labelled by subindices 1, 2, and 3 is shown in Figure 1b. Hopping terms corresponding to processes between the same kind of atoms, \(M\)-\(M\) or \(X\)-\(X\) (see Figure 1b), are given by  
\[t_{1}^{MM}=\frac{1}{4} \begin{pmatrix}3V_{dd\delta}+V_{dd\sigma}& \frac{\sqrt{3}}{2}(-V_{dd\delta}+V_{dd\sigma})&-\frac{3}{2}(V_{dd\delta}-V_{ dd\sigma})\\ \frac{\sqrt{3}}{2}(-V_{dd\delta}+V_{dd\sigma})&\frac{1}{4}(V_{dd\delta}+12V_ {dd\pi}+3V_{dd\sigma})&\frac{\sqrt{3}}{4}(V_{dd\delta}-4V_{dd\pi}+3V_{dd\sigma })\\ -\frac{3}{2}(V_{dd\delta}-V_{dd\sigma})&\frac{\sqrt{3}}{4}(V_{dd\delta}-4V_{ dd\pi}+3V_{dd\sigma})&\frac{1}{4}(3V_{dd\delta}+4V_{dd\pi}+9V_{dd\sigma}) \end{pmatrix} , \tag{11}\]  
\[t_{2}^{MM}=\frac{1}{4} \begin{pmatrix}3V_{dd\delta}+V_{dd\sigma}& \sqrt{3}(V_{dd\delta}-V_{dd\sigma})&0\\ \sqrt{3}(V_{dd\delta}-V_{dd\sigma})&V_{dd\delta}+3V_{dd\sigma}&0\\ 0&0&4V_{dd\pi}\end{pmatrix} , \tag{12}\]  
\[t_{3}^{MM}=\frac{1}{4} \begin{pmatrix}3V_{dd\delta}+V_{dd\sigma}& \frac{\sqrt{3}}{2}(-V_{dd\delta}+V_{dd\sigma})&\frac{3}{2}(V_{dd\delta}-V_{ dd\sigma})\\ \frac{\sqrt{3}}{2}(-V_{dd\delta}+V_{dd\sigma})&\frac{1}{4}(V_{dd\delta}+12V_ {dd\pi}+3V_{dd\sigma})&-\frac{\sqrt{3}}{4}(V_{dd\delta}-4V_{dd\pi}+3V_{dd \sigma})\\ \frac{3}{2}(V_{dd\delta}-V_{dd\sigma})&-\frac{\sqrt{3}}{4}(V_{dd\delta}-4V_{ dd\pi}+3V_{dd\sigma})&\frac{1}{4}(3V_{dd\delta}+4V_{dd\pi}+9V_{dd\sigma}) \end{pmatrix} , \tag{13}\]  
\[t_{1}^{XX}=\frac{1}{4} \begin{pmatrix}3V_{pp\pi}+V_{pp\sigma}& \sqrt{3}(V_{pp\pi}-V_{pp\sigma})&0\\ \sqrt{3}(V_{pp\pi}-V_{pp\sigma})&V_{pp\pi}+3V_{pp\sigma}&0\\ 0&0&4V_{pp\pi}\end{pmatrix} , \tag{14}\]  
\[t_{2}^{XX}= \begin{pmatrix}V_{pp\sigma}&0&0\\ 0&V_{pp\pi}&0\\ 0&0&V_{pp\pi}\end{pmatrix} , \tag{15}\]  
\[t_{3}^{XX}=\frac{1}{4}