Nonlinear Hall effect in topological Dirac semimetals in parallel magnetic field

We compute the second-harmonic response of two-dimensional topological Dirac semimetals subjected to an external in-plane magnetic field. The quantum kinetic equation for the Wigner distribution function is derived and then solved to evaluate 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 WTe$_2$ and WSe$_2$ monolayers, as well as in the Kondo lattice material Ce$_3$Bi$_4$Pd$_3$ at very low temperatures.