  We have investigated the nature of surface states in the Bi2Te3 family of
three-dimensional topological insulators using first-principles calculations as
well as model Hamiltonians. When the surface Dirac cone is warped due to
Dresselhaus spin-orbit coupling in rhombohedral structures, the spin acquires a
finite out-of-plane component. We predict a novel in-plane spin-texture of the
warped surface Dirac cone with spins not perpendicular to the electron
momentum. Our k.p model calculation reveals that this novel in-plane
spin-texture requires high order Dresselhaus spin-orbit coupling terms.
