Thermoelectric transport in thin films of three-dimensional topological insulators

We numerically study the thermoelectric transport properties based on the Haldane model of the three-dimensional topological insulator (3DTI) thin film in the presence of an exchange field g and a hybridization gap ??. The thermoelectric coefficients exhibit rich behaviors as a consequence of the interplay between g and ?? in the 3DTI thin film. For ??=0 but g???0, the transverse thermoelectric conductivity ??xy saturates to a universal value 1.38kBe/h at the center of each Landau level (LL) in the high-temperature regime, and displays a linear temperature dependence at low temperatures. The semiclassical Mott relation is found to remain valid at low temperatures. If g=0 but ?????0, the thermoelectric coefficients are consistent with those of a band insulator. For both g???0 and ?????0, ??xy saturates to a universal value 0.69kBe/h at the center of each LL in the high-temperature regime. We attribute this behavior to the split of all the LLs, caused by the simultaneous presence of nonzero g and ??, which lifts the degeneracies between Dirac surface states