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Nonlinear Hall effects with an exceptional ring

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arxiv 2411.06509 v3 pith:BMP2OH3A submitted 2024-11-10 cond-mat.mes-hall

Fang Qin , Ruizhe Shen , Ching Hua Lee This is my paper · ORCID
classification cond-mat.mes-hall
keywords exceptionalnonlinearringberrygivehallnon-hermiticityresponse
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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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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Geometric origin of self-intersection points in non-Hermitian energy spectra

    quant-ph 2025-02 conditional novelty 6.0 of 10

    Self-intersection points in one-dimensional non-Hermitian energy spectra are shown to occur exactly where the auxiliary generalized Brillouin zone crosses the Brillouin zone.

  2. Yukawa-Lorentz Symmetry of Tilted Non-Hermitian Dirac Semimetals at Quantum Criticality

    cond-mat.str-el 2024-11 conditional novelty 6.0 of 10

    Using a one-loop epsilon expansion, the tilt and velocity anisotropy perturbations are shown to be irrelevant at the quantum critical point of non-Hermitian tilted Dirac semimetals, so Yukawa-Lorentz symmetry emerges.

  3. Nonlinear Hall Effect in Two-dimensional Materials

    cond-mat.mes-hall 2024-12 conditional novelty 1.0 of 10

    This review organizes the nonlinear Hall effect in 2D materials into four mechanisms, quantum metric dipole, Berry curvature dipole, side-jump, and skew scattering, and catalogs experimental observations and applications.

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