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The Hall effect goes nonlinear

A new type of Hall effect — a nonlinear planar Hall effect — has been observed in a 3D non-magnetic topological insulator in the presence of an external magnetic field, as Hyunsoo Yang and colleagues report in the Physical Review Letters.

Credit: Pan He, National University of Singapore, Singapore/Vicky Summersby, Springer Nature Limited

The conventional Hall effect, discovered in 1897, is driven by the Lorentz force, which acts on electrons moving through an electric and a magnetic field. It gives rise to a voltage that is proportional to the current and to the magnetic field strength, and is extremely useful for determining the sign and density of the charge carriers. Over the years, a number of different Hall effects have been discovered, such as the quantum, fractional and spin Hall effects.

The possibility of realizing a nonlinear Hall effect, in which the generated voltage scales quadratically rather than linearly with the current, was theoretically suggested in 2015. In the nonlinear Hall effect, a Hall current can be generated as a second-order response to an external electric field. Such a nonlinear Hall effect has been recently observed by two different groups in a non-magnetic system, few-layer WTe2, without the need to apply an external magnetic field.

Yang and colleagues now report on the observation of a nonlinear Hall effect in Bi2Se3, a non-magnetic topological insulator, in the presence of an in-plane magnetic field. The magnetic field can then be used as an external knob to control the generated Hall voltage, which can be advantageous for future applications.

3D topological insulators exhibit topologically protected surface states at their edges, where the carriers have their spins locked perpendicularly to their momenta. It is known that the surface states exhibit peculiar magnetotransport properties, but few studies so far have focused on the investigation of the Hall effect in such states. “Previously, we investigated a nonlinear magnetoresistance in Bi2Se3, which occurs along the current direction when an in-plane magnetic field is applied,” explains Pan He, first author of the study. “Intuitively, we expected a complementary effect in the transverse direction — that is, a nonlinear planar Hall effect — originating from the spin–momentum locking in the surface states.”

This nonlinear planar Hall effect arises intrinsically from the topological surface band structure of the material: it originates from the generation of a spin current in response to the second-order component of the electric field. Owing to spin–momentum locking, this spin current is converted into a nonlinear charge current when an in-plane magnetic field is applied. “This nonlinear planar Hall effect should exist in a wide class of non-centrosymmetric materials, opening up a new research area that may lead to fruitful new physics,” comments Yang. “Clearly, the nonlinear Hall effect, with or without a magnetic field, will attract substantial experimental and theoretical interest.”

“Clearly, the nonlinear Hall effect, with or without a magnetic field, will attract substantial experimental and theoretical interest”

Unlike linear Hall effects, the nonlinear Hall effect exhibits a component of the voltage oscillating at twice the frequency of the driving alternating current (the second-harmonic Hall voltage) and a steady component that is generated owing to the rectification effect, whereby an alternating-current signal is converted into a direct-current signal. Thus, nonlinear Hall effects could be exploited in applications that require second-harmonic generation or rectification, which are used, for example, in energy harvesting, wireless communications and IR detectors.


Original article

  1. He, P. et al. Nonlinear planar Hall effect. Phys. Rev. Lett. 123, 016801 (2019)

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Further reading

  1. Sodemann, I. et al. Quantum nonlinear Hall effect induced by Berry curvature dipole in time-reversal invariant materials. Phys. Rev. Lett. 115, 216806 (2015)

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  2. Ma, Q. et al. Observation of the nonlinear Hall effect under time-reversal-symmetric conditions. Nature 565, 337–342 (2019)

    CAS  Article  Google Scholar 

  3. Kang, K. et al. Nonlinear anomalous Hall effect in few-layer WTe2. Nat. Mater. 18, 324–328 (2019)

    CAS  Article  Google Scholar 

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Correspondence to Giulia Pacchioni.

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Pacchioni, G. The Hall effect goes nonlinear. Nat Rev Mater 4, 514 (2019).

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