Quantum Metric and Nonlinear Transport in Magnetic Topological Insulators*

The quantum geometry has significant consequences in determining transport and optical properties in quantum materials. Here, we use a semiclassical formalism unifying the nonlinear anomalous Hall effect (NLAHE) and nonreciprocal magnetoresistance (NMR, longitudinal resistance) from the quantum geometry. In the dc limit, both transverse and longitudinal nonlinear conductivities include a term due to the normalized quantum metric dipole. The quantum metric contribution is intrinsic and does not scale with the quasiparticle lifetime. We demonstrate the coexistence of a NLAHE and NMR in films of the doped antiferromagentic topological insulator MnBi2Te4, which is verified by a recent experiment. Our work indicates that both longitudinal and transverse nonlinear transport provide a sensitive probe of the quantum geometry in solids.