Symmetry predicted transitions in 3D topological insulators

• A novel symmetry based method designed for Topological Insulator materials to predict/interpret allowed/forbidden transitions.
• Specific selection rules are obtained for optical transitions of topics: surface–surface, bulk–surface and bulk–bulk.
• Proof that surface states are protected by spatial symmetry as well as the “topological protection”.

We performed group theoretical investigation on symmetries of excitations in 3D topological insulators (TI) Bi2Te3, Bi2Se3 and Sb2Te3. Selection rules of transitions from bulk states (BS) to bulk states, surface states (SS) to surface states and bulk states to surface states are studied over the entire Brillouin zone. A new representation group G′ is constructed to deal with transitions between surface states and bulk states. Both direct and indirect optical transitions are studied. We also derive selection rules for scattering between SS and phonons. Our group theory analysis shows that SS is protected from scattering by both spatial symmetry and topology: many SS scattering channels are forbidden by symmetry and topological protection further suppresses the symmetry allowed scattering. Our analysis can provide an explanation of some ARPES results and Raman experiments.