Gyrotropic Hall effect in Berry-curved materials

König, Elio J.; Dzero, Maxim; Levchenko, Alex; Pesin, D. A.

doi:10.1103/physrevb.99.155404

Cited by 65 publications

(55 citation statements)

References 48 publications

(98 reference statements)

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“…Away from the limit, the double- and zero-frequency nonlinear Hall conductivities have different frequency dependence, thus are different in general. For a complete description, we list the -dependent full expressions with and without time-reversal symmetry (Supplementary Note 3), which would be helpful for understanding the recently proposed high-frequency rectification 22 and gyrotropic Hall effects 23 . According to how disorder works, the formulas are classified in terms of intrinsic ( in ), side-jump ( sj ), skew-scattering ( sk ) contributions.…”

Section: Resultsmentioning

confidence: 99%

Disorder-induced nonlinear Hall effect with time-reversal symmetry

et al. 2019

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The nonlinear Hall effect has opened the door towards deeper understanding of topological states of matter. Disorder plays indispensable roles in various linear Hall effects, such as the localization in the quantized Hall effects and the extrinsic mechanisms of the anomalous, spin, and valley Hall effects. Unlike in the linear Hall effects, disorder enters the nonlinear Hall effect even in the leading order. Here, we derive the formulas of the nonlinear Hall conductivity in the presence of disorder scattering. We apply the formulas to calculate the nonlinear Hall response of the tilted 2D Dirac model, which is the symmetry-allowed minimal model for the nonlinear Hall effect and can serve as a building block in realistic band structures. More importantly, we construct the general scaling law of the nonlinear Hall effect, which may help in experiments to distinguish disorder-induced contributions to the nonlinear Hall effect in the future.

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Section: Resultsmentioning

confidence: 99%

Disorder-induced nonlinear Hall effect with time-reversal symmetry

et al. 2019

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“…We leave the discussion of extrinsic mechanisms for a future work. For time-reversal invariant systems, this has been worked out recently [56][57][58]. We emphasize that scattering induced processes can be comparable in size to the response due to band structure effects [39,51].…”

Section: A Overviewmentioning

confidence: 99%

Consequences of time-reversal-symmetry breaking in the light-matter interaction: Berry curvature, quantum metric, and diabatic motion

Holder

Kaplan

Yan

2020

Phys. Rev. Research

110

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Nonlinear optical response is well studied in the context of semiconductors and has gained a renaissance in studies of topological materials in the recent decade. So far it mainly deals with nonmagnetic materials and it is believed to root in the Berry curvature of the material band structure. In this work we revisit the general formalism for the second-order optical response and focus on the consequences of the time-reversal-symmetry (T) breaking, by a diagrammatic approach. We have identified three physical mechanisms to generate a DC photocurrent, i.e., the Berry curvature, a term closely related to the quantum metric, and the diabatic motion. All three effects can be understood intuitively from the anomalous acceleration. The first two terms are respectively the antisymmetric and symmetric parts of the quantum geometric tensor. The last term is due to the dynamical antilocalization that appears from the phase accumulation between time-reversed fermion loops. Additionally, we derive the semiclassical conductivity that includes both intra-and interband effects. We find that T breaking can lead to a greatly enhanced nonlinear anomalous Hall effect that is beyond the contribution by the Berry curvature dipole.

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“…It has recently been proposed that the nonlinear Hall effect can also be used to probe the quantum critical point 3 , 6 , 17 and Néel vector orientation in antiferromagnets 18 . Various related phenomena have also been proposed, such as the gyrotropic Hall effect 30 , the Magnus Hall effect 31 , and the nonlinear Nernst effect 32 , 33 .…”

Section: Introductionmentioning

confidence: 99%

Quantum theory of the nonlinear Hall effect

Wang

Sun

et al. 2021

Nat Commun

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The nonlinear Hall effect is an unconventional response, in which a voltage can be driven by two perpendicular currents in the Hall-bar measurement. Unprecedented in the family of the Hall effects, it can survive time-reversal symmetry but is sensitive to the breaking of discrete and crystal symmetries. It is a quantum transport phenomenon that has deep connection with the Berry curvature. However, a full quantum description is still absent. Here we construct a quantum theory of the nonlinear Hall effect by using the diagrammatic technique. Quite different from nonlinear optics, nearly all the diagrams account for the disorder effects, which play decisive role in the electronic transport. After including the disorder contributions in terms of the Feynman diagrams, the total nonlinear Hall conductivity is enhanced but its sign remains unchanged for the 2D tilted Dirac model, compared to the one with only the Berry curvature contribution. We discuss the symmetry of the nonlinear conductivity tensor and predict a pure disorder-induced nonlinear Hall effect for point groups C3, C3h, C3v, D3h, D3 in 2D, and T, Td, C3h, D3h in 3D. This work will be helpful for explorations of the topological physics beyond the linear regime.

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Gyrotropic Hall effect in Berry-curved materials

Cited by 65 publications

References 48 publications

Disorder-induced nonlinear Hall effect with time-reversal symmetry

Disorder-induced nonlinear Hall effect with time-reversal symmetry

Consequences of time-reversal-symmetry breaking in the light-matter interaction: Berry curvature, quantum metric, and diabatic motion

Quantum theory of the nonlinear Hall effect

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