Bilinear planar Hall effect in topological insulators due to spin-momentum locking inhomogeneity

TL;DR

This paper investigates how inhomogeneity in spin-momentum locking affects the planar Hall effect in topological insulators, revealing a dominant nonlinear bilinear component due to inhomogeneity.

Contribution

It introduces a theoretical model showing the emergence of a nonlinear bilinear planar Hall effect caused by spin-momentum locking inhomogeneity in topological insulators.

Findings

Nonlinear planar Hall conductivity changes sign with current or magnetic field reversal.

Nonlinear term dominates over conventional planar Hall effect in certain conditions.

The effect arises from spin-momentum locking inhomogeneity in isotropic topological insulators.

Abstract

We study the effect of spin-momentum locking inhomogeneity on the planar Hall effect in topological insulators (TIs). Using the minimal model describing surface states of 3D TIs and semiclassical Boltzmann formalism, we have derived the planar Hall conductivity within the generalized relaxation time approximation. We have found that the total planar Hall conductivity is a sum of linear and nonlinear to the external electric field components. The linear term is a conventional planar Hall conductivity which scales quadratically with an external magnetic field, whereas the nonlinear term reveals bilinear behaviour, i.e., changes its sign when either charge current density or in-plane magnetic field orientation is reversed. We have 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 under the conventional planar Hall effect.