We compute the second-harmonic response of two-dimensional topological Dirac semimetals subjected to an in-plane magnetic field. The quantum kinetic equation for the Wigner distribution function is derived and then solved to compute the second-order electric-field contributions to the current density. Both the Berry curvature dipole and the field-induced terms in the current are analyzed across a broad range of model parameters. We propose that our theory can be tested experimentally by measuring the dependence of the anomalous Hall resistivity on the in-plane magnetic field in the surface states of the topological insulator SnTe, in ${\mathrm{WTe}}_2$ and ${\mathrm{WSe}}_2$ monolayers, as well as under applied uniaxial stress in the Kondo lattice material ${\mathrm{Ce}}_3{\mathrm{Bi}}_4{\mathrm{Pd}}_3$ at very low temperatures.

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• Electrical conductivity
• Geometric & topological phases
• Magneto-optics
• Mesoscopics
• Optical conductivity