Theory for linear and nonlinear planar Hall effect in topological insulator thin films

Recently, the linear and nonlinear planar Hall effect (PHE) on the topological insulators (TIs) surface has been extensively studied in experiments. To explain this phenomenon, various microscopic mechanisms are proposed theoretically, and one has to employ different mechanisms to separately understand the linear and nonlinear PHE even for the same system. Here, we study the planar magnetic resistance effect in TI thin film and find that a peculiar anisotropic scattering and a spin valve structure with respect to the PHE can be caused by the tilt and shift of Dirac cones, respectively, which are induced by the combination of spin-momentum locking of surface states and an in-plane magnetic field. The tilt and shift effects can act as the origin of both the linear and nonlinear PHE by distorting the spin texture of surface states or forming the spin polarization. These two mechanisms interplay and dominate, respectively, in strong coupling (thin TI) and decoupling (thick TI) between bottom and top surfaces. For thick TI film, we show that both the linear and nonlinear PHEs induced by the tilt effect can recover the results observed in recent experiments. Our theory provides a perspective to understand the origin of both linear and nonlinear PHE observed in recent experiments.