Bilinear Planar Hall Effect in Topological Insulators Due to Spin-Momentum Locking Inhomogeneity

Herein, the effect of spin-momentum locking inhomogeneity on the planar Hall effect in topological insulators (TIs) is studied. Using the minimal model describing surface states of 3D TIs and semiclassical Boltzmann formalism, the planar Hall conductivity (PHC) within the generalized relaxation time approximation is derived. Herein, it is found that the total PHC consists of linear and nonlinear (in electric field) components. The linear term is a conventional PHC which scales quadratically with an external magnetic field, whereas the nonlinear term reveals bilinear behavior, that is, changes its sign when either charge current density or in-plane magnetic-field orientation is reversed. It is shown that the emergent nonlinear planar Hall effect is a consequence of spin-momentum locking inhomogeneity in the TIs with isotropic energy dispersion, and dominates over the conventional planar Hall effect.