Longitudinal nonlinear response plays a crucial role in nonreciprocal charge transport, and it may provide a simple electrical means to probe spin-orbit coupling, magnetic order, and polarization states, etc. Here, we report on a study on the polarization and magnetic field control of longitudinal nonlinear transport in two-dimensional (2D) ferroelectrics with in-plane polarization. Based on the Boltzmann transport theory, we first study this using a general Hamiltonian model, and we show that the nonlinear conductivity can be significantly tuned by the polarization and magnetic field. In addition, the nonlinear conductivity reveals a strong spatial anisotropy. We further derive the analytical formulas for the anisotropic nonlinear conductivity in exact accordance with numerical results. Then, we exemplify those phenomena in the 2D ferroelectric SnTe monolayer in the presence of an external magnetic field based on density functional theory calculations. It is also revealed that the polarity of nonlinear conductivity is locked in the direction of polarization, thus pointing to the feasibility of the nonlinear detection of polarization states. Our work uncovers intriguing features of the longitudinal nonlinear transport in 2D ferroelectrics, and it provides guidelines for designing the polarization control of rectifying devices.

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• Electrical conductivity
• Spin-orbit coupling
• Ferroelectrics
• Monolayer films
• Boltzmann theory
• First-principles calculations