We have considered theoretically nonlinear transport phenomena known as bilinear magnetoresistance (BMR) and nonlinear planar Hall effect (NPHE) within the effective model describing surface states of a 3D topological insulator. Both phenomena can occur in nonmagnetic materials with strong spin-orbit interaction and reveal a term that depends linearly on the charge current density (external electric field) and in-plane magnetic field. In earlier studies, the physical mechanism of BMR and NPHE was related to scattering on spin-momentum locking inhomogeneities or to the hexagonal warping of Dirac cones. Here, we focus on another mechanism related to scattering on impurities that inherently contain spin-orbit coupling. Using the Green's function formalism and diagramatic method, we have derived analytical results for diagonal and transverse conductivities and determined nonlinear signals. The analytical and numerical results on BMR and NPHE indicate the possibility of determining the material constants, such as the Fermi wave vector and spin-orbit coupling parameter, by simple magnetotransport measurements.

中文翻译：

---

拓扑绝缘体中的双线性磁阻和平面霍尔效应：自旋轨道杂质散射与非平衡自旋极化的相互作用

我们在描述 3D 拓扑绝缘体表面状态的有效模型中考虑了理论上的非线性输运现象，称为双线性磁阻 (BMR) 和非线性平面霍尔效应 (NPHE)。这两种现象都可以发生在具有强自旋轨道相互作用的非磁性材料中，并揭示了一个线性依赖于电荷电流密度（外部电场）和面内磁场的项。在早期的研究中，BMR和NPHE的物理机制与自旋动量锁定不均匀性的散射或狄拉克锥体的六边形扭曲有关。在这里，我们关注与固有地包含自旋轨道耦合的杂质散射有关的另一种机制。使用格林函数形式和图解方法，我们得出了对角电导率和横向电导率的分析结果并确定了非线性信号。 BMR 和 NPHE 的分析和数值结果表明可以通过简单的磁输运测量来确定材料常数，例如费米波矢量和自旋轨道耦合参数。