# Definition Consider this example of Bi$_2$Se$_3$ ([[Bi2Se3]]). Without spin-orbit coupling (left side of the figure), the blue band is made of Se $p_z$ orbitals and the red band is made of Bi $p_z$ orbitals. When you turn on [[Spin-Orbit Coupling|SOC]], you gap the system and the bands have conduction/valence bands now have mixed contributions. This is a very simple schematic of band inversion. ![[u87AG.jpg]] # Topological Insulators Band inversion is a necessary but not sufficient condition to have a topological insulator. # Resources [Matter Modeling Stack Exchange](https://mattermodeling.stackexchange.com/questions/909/what-is-band-inversion-and-how-to-recognize-it-in-band-structure)