Paper detail

Hot-carrier transport and spin relaxation on the surface of topological insulator

We study the charge and spin transport under high electric field (up to several kV/cm) on the surface of topological insulator Bi$_2$Se$_3$, where the electron-surface optical phonon scattering dominates except at very low temperature. Due to the spin mixing of conduction and valence bands, the electric field not only accelerates electrons in each band, but also leads to inter-band precession. In the presence of the electric field, electrons can transfer from the valence band to the conduction one via the inter-band precession and inter-band electron-phonon scattering. The electron density in each band varies with the electric field linearly when the electric field is strong. Due to the spin-momentum locking, a transverse spin polarization, with the magnitude proportional to the momentum scattering time, is induced by the electric field. The induced spin polarization depends on the electric field linearly when the latter is small. Moreover, its magnitude is inversely proportional to the temperature and is insensitive to the electron density at high temperature. Our investigation also reveals that due to the large relative static dielectric constant, the Coulomb scattering is too weak to establish a drifted Fermi distribution with a unified hot-electron temperature in the steady state under the electric field. After turning off the electric field in the steady state, the hot carriers cool down in a time scale of energy relaxation which is very long (of the order of 100-1000 ps) while the spin polarization relaxes in a time scale of momentum scattering which is quite short (of the order of 0.01-0.1 ps).