Effect of surface state hybridization on current-induced spin-orbit torque in thin topological insulator films

We investigate the current-induced spin-orbit torque in thin topological insulator (TI) films in the presence of hybridization between the top and bottom surface states. We formulate the relation between spin torque and TI thickness, from which we derived the optimal value of the thickness to maximize the torque. We show numerically that in typical TI thin films made of $mathrm{Bi_2Se_3}$, the optimal thickness is about 3-5 nm.