It is worth noting that stronger SOC interactions could lead to more inverted bands in any material, despite not being the dominant band inversion mechanism. We show this by tuning the SOC strength in SnTe (see computational details in Section 5.3.2). As shown in Figure , doubling the SOC strength in SnTe results in a larger separation of the valence and conduction band edges at the L-point, even leading to an off-centering of the band edges in the L-Γ direction. We therefore conclude that band inversion can be intensified (i.e. M0 in Eq. 1 can be made more negative) by strengthening either atomic orbital interactions or SOC in a system, or both. Spin-orbit effects play an additional role in topological insulators, which is to open a band gap in the bulk electronic structure as in Figure . Band inversion leads to a crossing (or "nodal line") between the valence and conduction bands in the absence of SOC, where the crossing is maintained because bands of opposite spins are not coupled. A band gap generally forms when bands of opposite spin components interact due to SOC, except in special cases where band crossings are protected by crystallographic symmetries. As a result, SOC plays two distinct roles in the context of band inversion-driven warping: (1) strong SOC can assist the inversion of the bands along with atomic orbital interactions (Figure ), and ( ) SOC can open a gap along band crossings in materials with inverted bands (Figure ).