In non-Hermitian band structures, exceptional points generically form gapless lines or loops that give rise to extensively many defective eigenstates. In this work, we investigate how they nontrivially contribute to higher-order nonlinear responses by introducing unique singularities in the Berry curvature dipole (BCD) or Berry connection polarizability (BCP). Using a tilted two-dimensional dissipative Dirac model ansatz that harbors an exceptional ring, broken inversion symmetry is shown to give rise to extrinsic (BCD) and intrinsic (BCP) nonlinear Hall behaviors unique to systems with extensive exceptional singularities. In particular, when the non-Hermiticity is increased while keeping the ring radius fixed, the BCD response exhibits a power-law increase, while the BCP response correspondingly decreases. Our work sheds light on how non-Hermiticity can qualitatively control the extent and nature of higher harmonic generation in solids.

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• Hall effect
• Quantum transport
• 2-dimensional systems
• Exceptional points
• Non-Hermitian systems
• Boltzmann theory
• Inversion symmetry