General nonlinear Hall current in magnetic insulators beyond the quantum anomalous Hall effect

Kaplan, Daniel; Holder, Tobias; Yan, Binghai

doi:10.21203/rs.3.rs-2072615/v1

Cited by 5 publications

(5 citation statements)

References 54 publications

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“…A similar reformulation as the one demonstrated here might be possible for higher-order response functions, which can serve to illuminate the physical origin of the recently demonstrated corrections to the quantum anomalous Hall effect 55 .…”

Section: Discussionmentioning

confidence: 57%

The quantum geometric origin of capacitance in insulators

Komissarov,

Holder,

Queiroz

2024

Nat Commun

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In band insulators, without a Fermi surface, adiabatic transport can exist due to the geometry of the ground state wavefunction. Here we show that for systems driven at a small but finite frequency ω, transport likewise depends sensitively on quantum geometry. We make this statement precise by expressing the Kubo formula for conductivity as the variation of the time-dependent polarization with respect to the applied field. We find that at linear order in frequency, the longitudinal conductivity results from an intrinsic capacitance determined by the ratio of the quantum metric and the spectral gap, establishing a fundamental link between the dielectric response and the quantum metric of insulators. We demonstrate that quantum geometry is responsible for the electronic contribution to the dielectric constant in a wide range of insulators, including the free electron gas in a quantizing magnetic field, for which we show the capacitance is quantized. We also study gapped bands of hBN-aligned twisted bilayer graphene and obstructed atomic insulators such as diamond. In the latter, we find its abnormally large refractive index to have a topological origin.

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Section: Discussionmentioning

confidence: 57%

The quantum geometric origin of capacitance in insulators

Komissarov,

Holder,

Queiroz

2024

Nat Commun

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“…At the same time, we find that the semiclassical expressions reported up to now have been incomplete, missing an important piece in σ ab; c τ 0 . As this additional contribution, in the form of η ab; c nn is non-dissipative (scales with τ 0 ) and Hall-like (vanishes when a = b = c), we explore it in a separate work [52]. We have also derived a new contribution σ a b; c τ −1 which is inaccessible in the semiclassical approach.…”

Section: Discussionmentioning

confidence: 99%

Unifying semiclassics and quantum perturbation theory at nonlinear order

2023

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Nonlinear electrical response permits a unique window into effects of band structure geometry. It can be calculated either starting from a Boltzmann approach for small frequencies, or using Kubo’s formula for resonances at finite frequency. However, a precise connection between both approaches has not been established. Focusing on the second order nonlinear response, here we show how the semiclassical limit can be recovered from perturbation theory in the velocity gauge, provided that finite quasiparticle lifetimes are taken into account. We find that matrix elements related to the band geometry combine in this limit to produce the semiclassical nonlinear conductivity. We demonstrate the power of the new formalism by deriving a quantum contribution to the nonlinear conductivity which is of order \tau^{-1}τ−1 in the relaxation time \tauτ, which is principally inaccessible within the Boltzmann approach. We outline which steps can be generalized to higher orders in the applied perturbation, and comment about potential experimental signatures of our results.

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“…We consider positive and negative Γ values to identify the magnetic origin of photocurrents. By analyzing the Γ-scaling of the photocurrents it is also possible to identify the role of different quantum geometric quantities 22,[43][44][45] . General understanding of current photo-response suggests that three terms can be identified which differ in their scaling behavior with respect to Γ: a Drude term quadratic in the lifetime broadening, a term probing the Berry curvature dipole which is linear in the lifetime broadening, and a term probing the quantum metric dipole independent on the lifetime broadening 22 .…”

Section: Effect Of Quasiparticle Lifetimementioning

confidence: 99%

Photocurrents, inverse Faraday effect and photospin Hall effect in Mn$_2$Au

Merte¹,

Freimuth²,

Go³

et al. 2023

Preprint

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Among antiferromagnetic materials, Mn 2 Au is one of the most intensively studied, and it serves as a very popular platform for testing various ideas related to antiferromagnetic magnetotransport and dynamics. Since recently, this material has also attracted considerable interest in the context of optical properties and optically-driven antiferromagnetic switching. In this work, we use first principles methods to explore the physics of charge photocurrents, spin photocurrents and inverse Faraday effect in antiferromagnetic Mn 2 Au. We predict the symmetry and magnitude of these effects, and speculate that they can be used for tracking the dynamics of staggered moments during switching. Our calculations reveal the emergence of large photocurrents of spin in collinear Mn 2 Au, whose properties can be understood as a result of a non-linear optical version of spin Hall effect − which we refer to as the photospin Hall effect − encoded into the relation between the driving charge and resulting spin photocurrents. Moreover, we suggest that even a very small canting in Mn 2 Au can give rise to colossal spin photocurrents which are chiral in flavor. We conclude that the combination of staggered magnetization with the structural and electronic properties of this material results in a unique blend of prominent photocurrents, which makes Mn 2 Au a unique platform for advanced optospintronics applications.

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General nonlinear Hall current in magnetic insulators beyond the quantum anomalous Hall effect

Cited by 5 publications

References 54 publications

The quantum geometric origin of capacitance in insulators

The quantum geometric origin of capacitance in insulators

Unifying semiclassics and quantum perturbation theory at nonlinear order

Photocurrents, inverse Faraday effect and photospin Hall effect in Mn$_2$Au

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