Magnetic control of nonlinear transport induced by the quantum metric

The 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 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. Our work shines more light on the interplay between the nonlinear transport and quantum geometry.