Origin of planar Hall effect on the surface of topological insulators: Tilt of Dirac cone by an in-plane magnetic field

Recently, a novel planar Hall effect (PHE), which results from the resistivity anisotropy induced by an in-plane magnetic field, was discovered on the surface of topological insulators (TIs). While the PHE phenomenon in Weyl/Dirac semimetals is understood as a consequence of the chiral anomaly, the origin of the PHE in TIs, however, remains unclear theoretically. Several theories and experiments have ascribed the appearance of the PHE to the anisotropic backscattering induced by magnetic disorders, where the magnetization of the scatterers is indispensable. Instead, we here show that the anisotropic backscattering can arise from the tilt of the Dirac cone by an in-plane magnetic field, which emerges if nonlinear momentum terms are included, irrelevant to the magnetic nature of the scatterers. We further find that a relatively strong scalar potential can further enhance the PHE magnitude significantly, and the resulting impurity resonant state together with the tilted cone can produce the double-peak structure of the PHE and the sign change of the anisotropic magnetoresistivity. Our theory provides another perspective to understand the nontopological origin of the experimentally observed PHE in topological materials.