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In this paper, we investigate theoretically the spin-orbit torque as well asthe Gilbert damping for a two band model of a 2D helical surface state with aFerromagnetic (FM) exchange coupling. We decompose the density matrix into theFermi sea and Fermi surface components and obtain their contributions to theelectronic transport as well as the spin-orbit torque (SOT). Furthermore, weobtain the expression for the Gilbert damping due to the surface state of a 3DTopological Insulator (TI) and predicted its dependence on the direction of themagnetization precession axis.

Ferromagnetic Damping/Anti-damping in a Periodic 2D Helical surface; A Non-Equilibrium Keldysh Green Function Approach