A Design Scheme for Topological Insulators based Bonds, Bands, Symmetry and Spin Orbit Coupling

We report about a design scheme for topological insulators from the viewpoint of materials science or solid state chemistry. Topological insulators are a nice example for theory guided materials research. The electronic structure can be translated into the language of chemistry. The symmetry of the crystal- and the band structure, orbitals and spin orbit coupling determine whether a semiconductor is topologic or trivial. In this paper we will discuss the necessary and sufficient conditions for new TI materials, based in symmetry and bonding arguments.