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arXiv · 2209.15442

Third-order intrinsic anomalous Hall effect with generalized semiclassical theory

Longjun Xiang·Chao Zhang·Luyang Wang·Jian Wang
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Abstract

The linear intrinsic anomalous Hall effect (IAHE) and second-order IAHE have been intensively investigated in time-reversal broken systems. However, as one of the important members of the nonlinear Hall family, the investigation of third-order IAHE remains absent due to the lack of an appropriate theoretical approach, although the third-order extrinsic AHE has been studied within the framework of first- and second-order semiclassical theory. Herein, we generalize the semiclassical theory for Bloch electrons under the uniform electric field up to the third-order using wavepacket method and based on which we predict that the third-order IAHE can also occur in time-reversal broken systems. Same as the second-order IAHE, we find the band geometric quantity, the second-order field-dependent Berry curvature arising from the second-order field-induced positional shift, plays a pivotal role to observe this effect. Moreover, with symmetry analysis, we find that the third-order IAHE, as the leading contribution, is supported by 15 time-reversal broken 3D magnetic point groups (MPGs), corresponding to a wide class of antiferromagnetic (AFM) materials. Guided by the symmetry arguments, a two-band model is chosen to demonstrate the generalized theory. Furthermore, the generalized third-order semiclassical theory depends only on the properties of Bloch bands, implying that it can also be employed to explore the IAHE in realistic AFM materials, by combining with first-principles calculations.

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Longjun Xiang, Chao Zhang, Luyang Wang, Jian Wang. 2022-09-30. Third-order intrinsic anomalous Hall effect with generalized semiclassical theory. https://doi.org/10.1103/physrevb.107.075411

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