Spin-Seebeck effect due to thermally driven spin-polarized electron transport on the surface of a three-dimensional topological insulator

We study the spin Seebeck effect on the surface of a three-dimensional topological insulator (TI), such as Bi$_2$Se$_3$, in a geometry in which temperature bias is applied parallel to the surface. This generates spin-polarized charge current with polarization component $P_x \simeq 60\%$ along the direction of transport due to surface spin-orbit coupling. The spin current injected from the surface into a third nonmagnetic voltage probe, covering portion of the TI surface across its width, is converted via the inverse spin Hall effect (ISHE) into the voltage signal yielding the spin-Seebeck coefficient \mbox{$|S_{xy}|^{\mathrm{max}} \simeq 30$ nV/K} (assuming the SH angle of Pt voltage probe). Our prediction relies crucially on specific orientation of quintuple layers of Bi$_2$Se$_3$ with respect to the TI surface and direction of transport, as well as on the corresponding proper coupling of electronic spin states with support on the Bi and Se sublattice to spins emitted or absorbed by the three attached normal metal leads.