We investigate the nonlinear Hall responses in tunable two-dimensional Dirac materials. In particular, we study quantum geometry-driven second and third-order nonlinear responses in a time-reversal symmetric Dirac semimetal that can host a single-node, a double-node, and a nodal-ring depending on the model parameters. We find that the second-order Hall (SOH) response, which originates from the Berry curvature dipole, is enhanced in the single-node semimetallic phase as compared with the double-node case when inversion symmetry is broken. In contrast, the SOH response vanishes in the nodal-ring semimetal because the inversion symmetry is retained. Notably, the third-order Hall response arising from Berry connection polarizability becomes much larger in the nodal-ring 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.

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• Berry curvature
• Hall effect
• Dirac semimetal
• Nodal-line semimetals