Effective Hamiltonian for surface states of topological insulator thin films with hexagonal warping

The effective Hamiltonian of the surface states on semi-infinite slabs of the topological insulators (TI) Bi2Te3 and Bi2Se3 require the addition of a cubic momentum hexagonal warping term on top of the usual Dirac fermion Hamiltonian in order to reproduce the experimentally measured constant energy contours at intermediate values of Fermi energy. In this work, we derive the effective Hamiltonian for the surface states of a Bi2Se3 thin film incorporating the corresponding hexagonal warping terms. We then calculate the dispersion relation of the effective Hamiltonian and show that the hexagonal warping leads distorts the equal energy contours from the circular cross sections of the Dirac cones.