Transverse magnetic heat transport on the surface of a topological insulator

We investigate the Nernst-Ettingshausen and thermal Hall effects on the surface of a topological insulator on which a ferromagnet is attached. We present general expressions of the Peltier and the thermal Hall conductivities, which are reduced to simple forms at low temperatures. It is shown that the Peltier and the thermal Hall conductivities show nonmonotonic dependence on temperature. At low temperatures, they have a linear dependence on temperature. From the behavior of the Peltier conductivity at low temperatures, one can estimate the magnitude of the gap induced by time-reversal symmetry breaking. Moreover, we find that the Peltier conductivity can be used to map the Berry phase structure. These results open up the possibility of controlling transverse heat transport magnetically.

Figure 1

Schematic of the model (upper) and the dispersion of a massive Dirac fermion (lower).

Figure 2

Peltier conductivity ${\alpha }_{\mathit{xy}}$ in units of $k_{B}e/h$ (left panels), and normalized thermal Hall conductivity ${\kappa }_{\mathit{xy}}/\Delta$ in units of $k_B^2/h$ (right panels). Thin black lines in the upper panels represent the chemical potential as a function of $T$ for fixed electron densities. In the lower panels, we show the temperature dependence at $\mu /\Delta =2$ (lower left) and at $\mu /\Delta =0.5$ (lower right). The straight lines in the lower panels represent the low-temperature asymptotic behavior in Eqs. (11) and (13).