Nonlinear Hall effects with an exceptional ring

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.

21 pages, 6 figures, updated references, published version

References in corpus (20)

• The physics of exceptional points
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Topological Quantum Matter with Ultracold Gases in Optical Lattices
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Quantum metric nonlinear Hall effect in a topological antiferromagnetic heterostructure
• Topological invariance and global Berry phase in non-Hermitian systems
• The Berry curvature dipole in Weyl semimetal materials: an ab initio study
• Band signatures for strong nonlinear Hall effect in bilayer WTe${}_2$
• Tunable non-reciprocal quantum transport through a dissipative Aharonov-Bohm ring in ultracold atoms
• Non-Bloch topological invariants in a non-Hermitian domain-wall system
• Quantum frequency doubling in the topological insulator Bi2Se3
• Abelian and Non-Abelian Quantum Geometric Tensor
• High-Harmonic Generation from Monolayer and Bilayer Graphene
• Quantum geometry in condensed matter
• Fluctuations, uncertainty relations, and the geometry of quantum state manifolds
• Terahertz Polarization Conversion from Optical Dichroism in a Topological Dirac Semimetal
• How massless are Weyl fermions in Weyl semimetals?
• Intrinsic nonlinear conductivity induced by quantum geometry in altermagnets and measurement of the in-plane Néel vector
• Nonlinear Hall Effect in Two-dimensional Materials
• Polaron in a $p+ip$ Fermi topological superfluid

Cited by in corpus (4)

• Direct measurement of the quantum geometric tensor in pseudo-Hermitian systems
• Linear magnetoresistance of two-dimensional massless Dirac fermions in the quantum limit
• Emergent Weyl-like points in periodically modulated systems
• Exceptional rings in nonlinear non-Hermitian planar optical microcavities: implementation, signal enhancement, and topology