Nonlinear Hall effects with an exceptional ring

TL;DR

This paper explores how non-Hermitian topological features like exceptional rings influence nonlinear Hall effects, revealing unique responses and control mechanisms for higher harmonic generation in dissipative systems.

Contribution

It introduces the role of exceptional rings in non-Hermitian systems and their impact on nonlinear Hall responses, a novel insight into topological effects in dissipative materials.

Findings

Non-Hermitian exceptional rings induce unique nonlinear Hall behaviors.

Increasing non-Hermiticity enhances BCD response with a power-law trend.

BCP response decreases as non-Hermiticity increases.

Abstract

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.