Current density in anomalous Hall effect regime under weak scattering

doi:10.1088/1674-1056/adcd42

中国物理B ›› 2025, Vol. 34 ›› Issue (7): 77301-077301.doi: 10.1088/1674-1056/adcd42

Current density in anomalous Hall effect regime under weak scattering

Ning Dai(戴凝)^1,2,† and Bin Zhou(周斌)^1,2

1 Department of Physics, Hubei University, Wuhan 430062, China;
2 Key Laboratory of Intelligent Sensing System and Security of Ministry of Education, Hubei University, Wuhan 430062, China

收稿日期:2025-02-11 修回日期:2025-04-08 接受日期:2025-04-16 出版日期:2025-06-18 发布日期:2025-06-30
通讯作者: Ning Dai E-mail:daining@hubu.edu.cn
基金资助:
We thank H L Li for helpful discussion. N Dai was supported by the National Natural Science Foundation of China (Grant No. 12304062). B Zhou was supported by the National Natural Science Foundation of China (Grant No. 12074107), the Program of Outstanding Young and Middle-aged Scientific and Technological Innovation Teams of Colleges and Universities in Hubei Province (Grant No. T2020001), and the Innovation Group Project of the Natural Science Foundation of Hubei Province of China (Grant No. 2022CFA012).

Current density in anomalous Hall effect regime under weak scattering

Ning Dai(戴凝)^1,2,† and Bin Zhou(周斌)^1,2

1 Department of Physics, Hubei University, Wuhan 430062, China;
2 Key Laboratory of Intelligent Sensing System and Security of Ministry of Education, Hubei University, Wuhan 430062, China

Received:2025-02-11 Revised:2025-04-08 Accepted:2025-04-16 Online:2025-06-18 Published:2025-06-30
Contact: Ning Dai E-mail:daining@hubu.edu.cn
Supported by:
We thank H L Li for helpful discussion. N Dai was supported by the National Natural Science Foundation of China (Grant No. 12304062). B Zhou was supported by the National Natural Science Foundation of China (Grant No. 12074107), the Program of Outstanding Young and Middle-aged Scientific and Technological Innovation Teams of Colleges and Universities in Hubei Province (Grant No. T2020001), and the Innovation Group Project of the Natural Science Foundation of Hubei Province of China (Grant No. 2022CFA012).

摘要/Abstract

摘要： A finite equilibrium current density arises in the anomalous Hall effect (AHE) as a result of time-reversal symmetry breaking, affecting both the differential current density and total current. In this paper, we illustrate the equilibrium current density in a ribbon-shaped system within the AHE regime, consisting of two sets of counterpropagating channels arranged in a zebra stripes pattern. While the middle channels are susceptible to scattering, the edge channels remain relatively robust. Despite this difference, all channels exhibit the same differential current density when subjected to a differential voltage across the two ends of the ribbon. When a differential voltage is applied to both sides of the ribbon, it results in a snaking pattern of differential current density forming across it. Furthermore, in a four-terminal device comprising the ribbon and two normal leads, it is found that Hall conductance is independent of ribbon width within certain scattering strengths due to the differences in robustness between middle and edge channels. These findings disclose the details of the AHE transport in a finite-sized system under weak scattering.

关键词: anomalous Hall effect, quantum transport, current density, non-equilibrium Green's function

Abstract: A finite equilibrium current density arises in the anomalous Hall effect (AHE) as a result of time-reversal symmetry breaking, affecting both the differential current density and total current. In this paper, we illustrate the equilibrium current density in a ribbon-shaped system within the AHE regime, consisting of two sets of counterpropagating channels arranged in a zebra stripes pattern. While the middle channels are susceptible to scattering, the edge channels remain relatively robust. Despite this difference, all channels exhibit the same differential current density when subjected to a differential voltage across the two ends of the ribbon. When a differential voltage is applied to both sides of the ribbon, it results in a snaking pattern of differential current density forming across it. Furthermore, in a four-terminal device comprising the ribbon and two normal leads, it is found that Hall conductance is independent of ribbon width within certain scattering strengths due to the differences in robustness between middle and edge channels. These findings disclose the details of the AHE transport in a finite-sized system under weak scattering.

Key words: anomalous Hall effect, quantum transport, current density, non-equilibrium Green's function

中图分类号: (Electronic transport in mesoscopic systems)

73.23.-b

72.10.-d (Theory of electronic transport; scattering mechanisms) 73.43.-f (Quantum Hall effects) 73.23.Ad (Ballistic transport)

Ning Dai(戴凝) and Bin Zhou(周斌). Current density in anomalous Hall effect regime under weak scattering[J]. 中国物理B, 2025, 34(7): 77301-077301.

Ning Dai(戴凝) and Bin Zhou(周斌). Current density in anomalous Hall effect regime under weak scattering[J]. Chin. Phys. B, 2025, 34(7): 77301-077301.

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Current density in anomalous Hall effect regime under weak scattering

Current density in anomalous Hall effect regime under weak scattering

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