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The Hall effect refers to the generation of a voltage in a direction perpendicular to the applied current. Since its discovery in 1879, the Hall effect family has become a huge group, and its in-depth study is an important topic in the field of condensed matter physics. The newly discovered nonlinear Hall effect is a new member of Hall effects. Unlike most of previous Hall effects, the nonlinear Hall effect does not need to break the time-reversal symmetry of the system but requires the spatial inversion asymmetry. Since 2015, the nonlinear Hall effect has been predicted and observed in several kinds of materials with a nonuniform distribution of the Berry curvature of energy bands. Experimentally, when a longitudinal alternating current (AC) electric field is applied, a transverse Hall voltage will be generated, with its amplitude proportional to the square of the driving current. Such a nonlinear Hall signal contains two components: one is an AC transverse voltage oscillating at twice the frequency of the driving current, and the other is a direct current (DC) signal converted from the injected current. Although the history of the nonlinear Hall effect is only a few years, its broad application prospects in fields of wireless communication, energy harvesting, and infrared detectors have been widely recognized. The main reason is that the frequency doubling and rectification of electrical signals via some nonlinear Hall effects are achieved by an inherent quantum property of the material - the Berry curvature dipole moment, and therefore do not have the thermal voltage thresholds and/or the transition time characteristic of semiconductor junctions/diodes. Unfortunately, the existence of the Berry curvature dipole moment has more stringent requirements for the lattice symmetry breaking of the system apart from the spatial inversion breaking, and the materials available are largely limited. This greatly reduces the chance to optimize the signal of the nonlinear Hall effect and limits the application and development of the nonlinear Hall effect. The rapid development of van der Waals stacking technology in recent years provides a brand new way to design, tailor and control the symmetry of lattice, and to prepare artificial moiré crystals with certain physical properties. Recently, both theoretical results and experimental studies on graphene superlattices and transition metal dichalcogenide superlattices have shown that artificial moiré superlattice materials can have larger Berry curvature dipole moments than those in natural non-moiré crystals, which has obvious advantages in generating and manipulating the nonlinear Hall effect. On the other hand, abundant strong correlation effects have been observed in two-dimensional superlattices. The study of the nonlinear Hall effect in two-dimensional moiré superlattices can not only give people a new understanding of the momentum space distribution of Berry curvatures, contributing to the realization of more stable topological transport, correlation insulating states and superfluidity states, but also expand the functional space of moiré superlattice materials which are promising for the design of new electronic and optoelectronic devices. This review paper firstly introduces the birth and development of the nonlinear Hall effect and discusses two mechanisms of the nonlinear Hall effect: the Berry curvature dipole moment and the disorder. Subsequently, this paper summaries some properties of two-dimensional moiré superlattices which are essential in realizing the nonlinear Hall effect: considerable Berry curvatures, symmetry breaking effects, strong correlation effects and tunable band structures. Next, this paper reviews theoretical and experimental progress of nonlinear Hall effects in graphene and transition metal dichalcogenides superlattices. Finally, the future research directions and potential applications of the nonlinear Hall effect based on moiré superlattice materials are prospected.
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Keywords:
- nonlinear Hall effect/
- moiré superlattice/
- two-dimensional materials/
- Berry curvature dipole
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机制 对称性要求*(二维体系) 信号方向 标度关系 贝里曲率偶极矩导致 C1,C1v 仅在霍尔方向 $ {V}_{\perp }^{2 w}/{\left({V}_{/ /}^{w}\right)}^{2}\propto {\sigma }_{xx}^{0} $ 无序导致 边跳作用 C1,C1v,C3,C3h,C3v,D3h,D3 各个方向都有 $ {V}_{\perp }^{2 w}/{\left({V}_{/ /}^{w}\right)}^{2}\propto {\sigma }_{xx}^{2} $ 斜散射 注:*表示此处旋转轴为z轴, 镜面v代表yz或xz平面, 镜面h代表xy平面. 
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体系 维度 主导机制 温度/K 最大
V2w/VVw/V Iw/A $V^{2w}/(V^w)^2 $$ /\rm V^{-1}$ $V^{2w}/(I^w)^2 $$ /\rm (V{\cdot}A^{-2})$ 双层WTe2[12] 2 贝里曲率偶极矩 10—100 $ 2 \times {10}^{-4} $ $ {1 \times 10}^{-2} $ $ {1 \times 10}^{-6} $ 2 $ {2 \times 10}^{8} $ 多层WTe2[13] 2 贝里曲率偶极矩& 斜散射 1.8—100 $ 2.5 \times {10}^{-5} $ $ 7 \times {10}^{-4} $ — 51 — 多层WTe2[86] 2 贝里曲率偶极矩 80 $ 9 \times {10}^{-6} $ — $ 8 \times {10}^{-6} $ $ 5 \times {10}^{-2} $ $ {1.4 \times 10}^{5} $ 双层MoTe2[87] 2 贝里曲率偶极矩& 斜散射 1.6—100 $ 1.3 \times {10}^{-4} $ — $ 9.7 \times {10}^{-5} $ $ 2 \times {10}^{-3} $ $ {1.4 \times 10}^{4} $ Bi2Se3[79] 2 斜散射 2—200 $ 1.5 \times {10}^{-5} $ — $ 1.5 \times {10}^{-3} $ — 6.7 LaAlO3/SrTiO3
异质结[93]2 贝里曲率偶极矩 1.5 $ 1.2 \times {10}^{-4} $ — $ 2 \times {10}^{-4} $ — $ {3 \times 10}^{3} $ WTe2(面内
直流电场中)[82]2 贝里曲率偶极矩 5—286 $ 8 \times {10}^{-6} $ — $ 5 \times {10}^{-5} $ — $ {3.2 \times 10}^{3} $ 有应力的WSe2[84] 2 贝里曲率偶极矩 50—140 $ 1.2 \times {10}^{-5} $ — $ 4.5 \times {10}^{-6} $ — $ {5.9 \times 10}^{5} $ 波纹状graphene[85] 2 贝里曲率偶极矩 1.5—15 $ 1.2 \times {10}^{-6} $ — $ 1.2 \times {10}^{-7} $ — $ {8.3 \times 10}^{7} $ Twisted double bilayer graphene[20] 2 贝里曲率偶极矩 1.5—25 $ 4 \times {10}^{-5} $ $ 1.3 \times {10}^{-4} $ $ 8 \times {10}^{-8} $ $ 2 \times {10}^{3} $ $ {6.3 \times 10}^{9} $ Graphene/BN
超晶格[24]2 斜散射 1.6—120 $ 1.3 \times {10}^{-4} $ $ 9 \times {10}^{-3} $ $ 5 \times {10}^{-6} $ 1.6 $ {5.2 \times 10}^{6} $ Twisted bilayer graphene[23] 2 斜散射 1.7—80 $ 1 \times {10}^{-3} $ $ 6 \times {10}^{-3} $ $ 1 \times {10}^{-6} $ $ 27 $ $ {1 \times 10}^{9} $ Twisted double bilayer graphene[21] 2 贝里曲率偶极矩& 斜散射 1.7—20 $ 2 \times {10}^{-3} $ — $ 1 \times {10}^{-6} $ — $ {2 \times 10}^{9} $ Twisted bilayer graphene[26] 2 贝里曲率偶极矩 1.5—80 $ 2.3 \times {10}^{-6} $ $ 6.8 \times {10}^{-4} $ $ 1 \times {10}^{-7} $ $ 5 \times {10}^{2} $ $ {2.3 \times 10}^{8} $ Twisted WSe2[30] 2 贝里曲率偶极矩 1.5-30 $ 2 \times {10}^{-2} $ $ 4 \times {10}^{-3} $ $ 5 \times {10}^{-11} $ $ 1.2 \times {10}^{3} $ $ {8 \times 10}^{18} $ WTe2/WSe2
超晶格[33]2 贝里曲率偶极矩 30—100 $ 1.5 \times {10}^{-3} $ — $ 1 \times {10}^{-6} $ — $ {1.5 \times 10}^{9} $ 多层MoTe2[71] 3 无序散射 2—40 $ 4 \times {10}^{-7} $ $ 2 \times {10}^{-3} $ — $ {10}^{-1} $ — WTe2块材[88] 3 贝里曲率偶极矩或无序散射 1.4—4.2 $ 1.8 \times {10}^{-6} $ — $ 4 \times {10}^{-3} $ — $ {1.1 \times 10}^{-1} $ Cd3As2[88] 3 贝里曲率偶极矩或无序散射 1.4-4.2 $ 7.5 \times {10}^{-7} $ — $ 3.5 \times {10}^{-3} $ — $ {6.1 \times 10}^{-2} $ NbP (Pt电极)[89] 3 无序散射 300—350 $ 9 \times {10}^{-5} $ — $ 5 \times {10}^{-5} $ — $ {3.6 \times 10}^{4} $ TaIrTe4[72] 3 贝里曲率偶极矩& 无序散射 2—300 $ 1 \times {10}^{-4} $ — $ 6 \times {10}^{-4} $ — $ {2.8 \times 10}^{2} $ Ce3Bi4Pd3[90] 3 贝里曲率偶极矩 0.4—4 $ 8 \times {10}^{-7} $ — $ 1 \times {10}^{-2} $ — $ {8 \times 10}^{-3} $ (Pb1–xSnx)1–yInyTe[91] 3 贝里曲率偶极矩 3—40 $ 4 \times {10}^{-8} $ — $ 6 \times {10}^{-5} $ — 11 Pb1–xSnxTe[74] 3 贝里曲率偶极矩 5—300 $ 1 \times {10}^{-3} $ — $ 3 \times {10}^{-5} $ — $ {1.1 \times 10}^{6} $ ZrTe5[75] 3 贝里曲率偶极矩 2—100 $ 1 \times {10}^{-5} $ $ 1.1 \times {10}^{-2} $ — $ 8 \times {10}^{-2} $ — BaMnSb2[76] 3 贝里曲率偶极矩 100—400 $ 4 \times {10}^{-4} $ — $ 2 \times {10}^{-4} $ — $ {1 \times 10}^{4} $ α-(BEDT-TTF)2I3[92] 3 贝里曲率偶极矩 4.2—40 $ 1.3 \times {10}^{-6} $ — $ 1 \times {10}^{-3} $ — 1.3 DownLoad:
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[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61] [62] [63] [64] [65] [66] [67] [68] [69] [70] [71] [72] [73] [74] [75] [76] [77] [78] [79] [80] [81] [82] [83] [84] [85] [86] [87] [88] [89] [90] [91] [92] [93] [94] [95] [96] [97] [98] [99] [100] [101] [102] [103] [104] [105] [106] [107] [108] [109] [110] [111] [112] [113] [114] [115] [116] [117] [118] [119] [120] [121] [122] [123] [124] [125] [126] [127] [128] [129] [130] [131] [132] [133] [134] [135] [136] [137] [138] [139] [140] [141] [142] [143] [144] [145] [146] [147] [148] [149] [150] [151] [152] [153] [154] [155] [156] [157] [158] [159] [160] [161] [162] [163] [164] [165] [166] [167] [168]
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