Topological Phase Diagram of Pb1-xSnxSe1-yTey Quaternary Compound

We reproduce the mirror Chern number phase diagram for the quaternary compound Pb1-xSnxSe1-yTey combining the accurate density functional theory and the tight-biding model. The tight-binding models are extracted from the ab initio results, adding constraints to reproduce the experimental results. By using the virtual crystalline approximation, we calculated the mirror Chern number as a function of the concentrations x and y. We report different Hamiltonians depending on whether we want to focus on the experimental band gap or the experimental topological transition. We calculate the transition line between the trivial insulating phase and the topological insulating phase, which agrees well with the experimental results. Finally, we add the predicted in the literature Weyl phase into the phase diagram, providing a complete topological phase diagram for the Pb1-xSnxSe1-yTey quaternary compound.