Spin-orbit coupling tuned crossover of gaped and gapless topological phases in the chalcopyrite HgSnX2(X=N/P):

The coupling between electron orbital momentum and spin momentum, known as spin-orbit coupling (SOC), is a fundamental origin of many fascinating physical phenomena. It holds paramount significance in topological materials. Our work has predicted the topological phase in Hg-based chalcopyrite compounds using the first principles density functional theory. The initial focus was on HgSnN$_2$, revealing it to be a nonmagnetic Weyl semimetal, while HgSnP$_2$ displayed characteristics of a strong topological insulator. What makes our work truly unique is that despite both compounds having the same SOC strength, they exhibit distinct topological phases due to the hybridization of bands. This finding prompted us to pursue another significant objective: understanding the correlation between topological phases and band hybridization within these intermetallic compounds. Our results indicate that we can tune the topological phase by manipulating SOC strength due to band hybridization between the dominant p orbitals of N or P and a minor contribution from Hg-$d$. This investigation stands as a remarkable illustration of the unique roles that hybridization plays in sculpting the topological properties of these compounds while simultaneously preserving their crystal symmetry and time reversal symmetry.