We develop an effective bulk model with a topological boundary condition to
study the surface states of topological insulators. We find that the Dirac
point energy, the band curvature and the spin texture of surface states are
crystal face-dependent. For a given face on a sphere, the Dirac point energy is
determined by the bulk physics that breaks p-h symmetry in the surface normal
direction and is tunable by surface potentials that preserve T symmetry.
Constant energy contours near the Dirac point are ellipses with spin textures
that are helical on the S/N pole, collapsed to one dimension on any side face,
and tilted out-of-plane otherwise. Our findings identify a route to engineering
the Dirac point physics on the surfaces of real materials.Comment: 4.1 pages, 2 figures and 1 tabl
