Spin-Seebeck effect on the surface of a topological insulator due to nonequilibrium spin-polarization parallel to the direction of thermally driven electronic transport

Abstract

We study the transverse spin-Seebeck effect (SSE) on the surface of a three-dimensional topological insulator (TI) thin film, such as Bi${}_{2}$Se${}_{3}$, which is sandwiched between two normal metal leads. The temperature bias $\ensuremath{\Delta}T$ applied between the leads generates surface charge current which becomes spin polarized due to strong spin-orbit coupling on the TI surface, with polarization vector acquiring a component ${P}_{x}\ensuremath{\simeq}60%$ parallel to the direction of transport. When the third nonmagnetic voltage probe is attached to the portion of the TI surface across its width ${L}_{y}$, pure spin current will be injected into the probe where the inverse spin Hall effect (ISHE) converts it into a voltage signal $|{V}_{\mathrm{ISHE}}{|}^{\mathrm{max}}/\ensuremath{\Delta}T\ensuremath{\simeq}2.5\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}$V/K (assuming the SH angle of the Pt voltage probe and ${L}_{y}=1$ mm). The existence of predicted nonequilibrium spin polarization parallel to the direction of electronic transport and the corresponding electron-driven SSE crucially relies on orienting quintuple layers (QLs) of Bi${}_{2}$Se${}_{3}$ orthogonal to the TI surface and tilted by ${45}^{\ensuremath{\circ}}$ with respect to the direction of transport. Our analysis is based on the Landauer--B\"uttiker-type formula for spin currents in the leads of a multiterminal quantum-coherent junction, which is constructed by using nonequilibrium Green function formalism within which we show how to take into account arbitrary orientation of QLs via the self-energy describing coupling between semi-infinite normal metal leads and the TI sample.