Magnetic control of nonlinear transport induced by the quantum metric

Quantum geometry plays a crucial role in the nonlinear transport of quantum materials. Here, we use the Boltzmann transport formalism to study the magnetic control of nonlinear transport induced by the quantum metric in two-dimensional systems with different types of spin-orbit coupling (SOC). It is shown that the nonlinear conductivity is strongly dependent on the direction of a field and reveals significant spatial anisotropy. Moreover, the field-direction-dependent relations are distinct for different SOCs. In addition, it is demonstrated that the contributions from the quantum metric and the Drude mechanism are distinguishable due to their opposite signs or distinct anisotropy relations. We further derive the analytical formulas for the anisotropic nonlinear conductivity, in exact agreement with numerical results. Finally, we exemplify those phenomena in the ${\mathrm{Ag}}_{2}\mathrm{Te}$ monolayer in the presence of an external magnetic field based on density functional theory calculations. Our work shines more light on the interplay between nonlinear transport and quantum geometry.