Thermoelectric transport in thin films of three-dimensional topological insulators

Abstract

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 $\ensuremath{\Delta}$. The thermoelectric coefficients exhibit rich behaviors as a consequence of the interplay between $g$ and $\ensuremath{\Delta}$ in the 3DTI thin film. For $\ensuremath{\Delta}=0$ but $g\ensuremath{\ne}0$, the transverse thermoelectric conductivity ${\ensuremath{\alpha}}_{xy}$ saturates to a universal value $1.38{k}_{B}e/h$ 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 $\ensuremath{\Delta}\ensuremath{\ne}0$, the thermoelectric coefficients are consistent with those of a band insulator. For both $g\ensuremath{\ne}0$ and $\ensuremath{\Delta}\ensuremath{\ne}0$, ${\ensuremath{\alpha}}_{xy}$ saturates to a universal value $0.69{k}_{B}e/h$ 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 $\ensuremath{\Delta}$, which lifts the degeneracies between Dirac surface states.