Magnetochiral anisotropy induced nonlinear planar Hall effect in topological insulator surface states

In an intriguing recent experiment, it has been found that the two-dimensional (2D) surface states of a three-dimensional (3D) strong topological insulator (TI) support a nonzero Hall voltage transverse to an applied electric field even when the external magnetic field is in the plane (i.e., the in-plane Lorentz force vanishes). This so-called planar Hall effect (PHE) of TI surface states is found to be nonlinear, i.e., the Hall voltage scales quadratically with the applied electric field and linearly with the in-plane magnetic field. In this paper, we calculate the nonlinear PHE for strong topological insulator surface states with broken particle-hole symmetry and warping and provide results that interpolate continuously between the Dirac and normal fermion regimes, which can be compared with future experiments.