Massive Dirac fermions and spin physics in an ultrathin film of topological insulator

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We study transport and optical properties of the surface states which lie in the bulk energy gap of a thin-film topological insulator. When the film thickness is comparable with the surface state decay length into the bulk, the tunneling between the top and bottom surfaces opens an energy gap and form two degenerate massive Dirac hyperbolas. Spin dependent physics emerges in the surface bands which are vastly different from the bulk behavior. These include the surface spin Hall effects, spin dependent orbital magnetic moment, and spin dependent optical transition selection rule which allows optical spin injection. We show a topological quantum phase transition where the Chern number of the surface bands changes when varying the thickness of the thin film.