Electronic structure of the side surface of Bi$_{2}$Se$_{3}$

We investigate the electronic band structure of a side surface geometry, other than the conventional [111] surface, of the topological insulator Bi$_{2}$Se$_{3}$ using the first-principles pseudopotential calculations. As Bi$_{2}$Se$_{3}$ is known to be a strong topological insulator, it is expected that an arbitrary surface would have the topological surface state characterized by Dirac-cone-like band dispersion and spin-momentum coupling. Here we indeed obtain surface states with linear band dispersion around the Gamma point, but with a strong anisotropy with different group velocities along different k-directions. Low energy effective hamiltonian is proposed, and physical implications of the anisotropic Dirac fermions are also discussed.