Interband-induced nonlinear Hall effect from adiabatic dynamics in Dirac systems

By combining the adiabatic dynamical approach with the Boltzmann equation, we identify an additional contribution to the second-order nonlinear Hall conductivity arising from interband transitions, which is qualitatively distinct from the Berry-curvature-dipole response and other intrinsic mechanisms. Using a two-dimensional tilted Dirac-cone model, we demonstrate that this contribution decreases monotonically with increasing Fermi energy, is enhanced by the Dirac-cone tilt, and is strongly suppressed by the band gap. Furthermore, comparison of the theoretical results with experimental measurements indicates that including both the adiabatically induced contribution and the Berry-curvature-dipole response yields good agreement with the experimental data, suggesting that the adiabatic interband mechanism may provide an important contribution to the nonlinear Hall response.