Spin texture on the warped Dirac-cone surface states in topological insulators

We have investigated the nature of surface states in the Bi ₂Te₃ family of three-dimensional topological insulators using first-principles calculations as well as a model Hamiltonian approach. When the surface Dirac cone is warped due to Dresselhaus spin-orbit coupling in rhombohedral structures, the spin acquires a finite out-of-the-plane component. We provide a simple, minimal model to describe the in-plane spin texture of the warped surface Dirac cone observed in experiments where spins are seen to be not aligned perpendicular to the electron momentum. Our k•p model calculation reveals that this in-plane spin texture requires fifth-order Dresselhaus spin-orbit coupling terms.