Berry curvature-induced emerging magnetic response in two-dimensional materials

Liu Yu-Ting; He Wen-Yu; Liu Jun-Wei; Shao Qi-Ming

doi:10.7498/aps.70.20202132

Abstract

The magnetic response in a two-dimensional material has received increasing attention in recent years. The magnetic effects and related quantum transport originate from Berry curvature, which is associated with crystal symmetry and many quantum effects including electrons’ orbital magnetism, spin-orbit coupling, and magnetoelectricity. The importance of studying the magnetic response in the two-dimensional material lies in two aspects. First, the magnetic response of two-dimensional material provides a platform to investigate the coupling between the above-mentioned intrinsic quantum effects and their couplings. Second, it possesses the potential applications in energy-efficient quantum and spintronic devices. Here, we review the experimental research progress made in recent years. In particular, we focus on the research progress of the valley Hall and magnetoelectric effect, quantum non-linear Hall effect, anomalous Hall, and quantum anomalous Hall effect in two-dimensional materials such as graphene, transition-metal chalcogenides, and twisted bilayer graphene. For each session, we first introduce these phenomena and their underlying physics by using crystal symmetries and band structures. Then, we summarize the experimental results and identify unsolved problems. At last, we provide an outlook in this emerging research direction.

Keywords:

Authors and contacts

1.
Department of Electronic and Computing Engineering, The Hong Kong University of Science and Technology, Hong Kong 999077, China
2.
Department of Physics, The Hong Kong University of Science and Technology, Hong Kong 999077, China

Corresponding author: Shao Qi-Ming, eeqshao@ust.hk

Funds: Project supported by the HK University Grant Committee (Grant Nos. ECS26200520, N_HKUST626/18, 26302118, 16305019), the HKUST ECE Start-up Fund, and the HKUST Postdoctoral Fellowship Matching Fund (Grant No. NA389)

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Cited By

图 1 受应力的单层硫化钼谷磁电效应示意图　(a)谷霍尔效应^[22]; (b)谷磁电效应^[25]; (c)自旋极化引起的磁矩和谷磁电性引起的磁矩在外磁场下的磁光克尔响应; (d)磁光克尔响应与施加电流方向和应力方向的关系

Figure 1. Sketch of the magnetoelectric effect in monolayer MoS₂: (a) Valley Hall effect^[22]; (b) valley magnetoelectricity^[25]; (c) comparison of magneto-optical Kerr response between spin polarizations induced magnetism and valley magnetization under external magnetic fields; (d) valley magnetization-induced Kerr rotation as a function of the azimuthal angle of current for zigzag and armchair monolayer MoS₂.

DownLoad: Full-Size Img PowerPoint

图 2 碲化钨中量子非线性霍尔效应示意图　(a)线性和非线性霍尔电压随电流的变化^[47]; (b)碲化钨在不同方向上的晶体结构示意图; (c)纵向电压和非线性霍尔电压与电流施加方向的关系^[27]; (d)非线性霍尔电压与材料电导率的关系. 插图表示了非线性霍尔效应的两种来源: 贝里曲率和电子偏散射输运^[27]

Figure 2. Illustration of the quantum nonlinear Hall effect: (a) Dependence of linear and non-linear Hall voltage on applied currents^[47]; (b) crystal structure of WTe₂; (c) angular dependence of longitudinal voltage and non-linear Hall voltage^[27]; (d) relationship between nonlinear Hall voltage and conductance. The inset shows two origins of nonlinear Hall voltage: Intrinsic Berry curvature and skew scattering^[27].

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图 3 转角双层石墨烯中量子反常霍尔效应示意图　(a)自旋磁化和轨道磁化中量子反常霍尔效应对比示意图; (b)转角双层石墨烯中自旋极化和能谷非极化的导带示意图; (c)转角双层石墨烯中自旋和能谷完全极化的导带示意图; (d)量子反常霍尔态下, 霍尔电阻和纵向电阻随磁场的变化关系, 插图表示材料的导电状态—边缘导电和体导电; (e)电流控制反常霍尔态下磁性翻转示意图

Figure 3. Illustration of quantum anomalous Hall effect in twisted bilayer graphene (tBLG): (a) Sketch of quantum anomalous Hall effect in spin magnetization and orbital magnetization systems; (b) schematic of fully spin-polarized and but valley-unpolarized conduction bands in a moiré unit cell of tBLG; (c) schematic of fully spin-polarized and valley-polarized conduction bands in a moiré unit cell of tBLG; (d) longitudinal resistance and Hall resistance as a function of magnetic field in the quantum anomalous Hall state, and the insets show the bulk and edge conduction states of material; (e) current control of magnetization switching in the anomalous Hall state.

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