Nonlinear Hall responses in tunable nodal Dirac semimetals

Abstract: We investigate the nonlinear Hall responses in tunable two-dimensional Dirac materials. In particular, we study quantum geometry-driven second and third order non-linear responses in a time-reversal symmetric Dirac semimetal that can host single, double and line nodes depending on the model parameters. We find that the second-order Hall response (SOHE), which originates from the Berry curvature dipole, is enhanced in the single-node semimetallic phase as compared to the double node case when inversion symmetry is broken. In contrast, the SOHE vanishes in the nodal line semimetal as the inversion symmetry retains. Notably, the third-order Hall response due to Berry connection polarizabilty becomes much larger in the line-node Dirac semimetal, especially when the Fermi energy lies near the band edge, than in the single- and double-node Dirac semimetals. The reason for this contrasting behavior is attributed to the distinct distribution of the Berry connection polarizability in the Brillouin zone.