In a previous study, we demonstrated that band warping and high valley degeneracy can be achieved through band inversion in rock-salt systems. However, several key questions regarding band inversion-driven warping and high valley degeneracy in topological insulators remain unanswered. First, it is not clear whether warping occurs due to band inversion in systems other than rock-salt materials, given our previous analysis was based on a k • p model specifically for this system. Second, the proposed mechanisms behind band inversion is inconsistent. While it is generally believed that the spin-orbit coupling (SOC) strength is largely responsible for the degree to which bands are inverted in systems such as tetradymite Bi2Te3, atomic orbital interactions (e.g. s-p coupling) have been suggested as a significant cona Department of Materials Science and Engineering, Northwestern University, Evanston, IL 60208.