REFERENCES

1. Rüter, C. E.; Makris, K. G.; El-Ganainy, R.; et al. Observation of parity-time symmetry in optics. Nat. Phys. 2010, 6, 192-5.

2. Liu, L.; Zhao, T.; Lin, W.; et al. Symmetry breaking for current-induced magnetization switching. Appl. Phys. Rev. 2023, 10, 021319.

3. Dembowski, C.; Dietz, B.; Graf, H. D.; et al. Observation of a chiral state in a microwave cavity. Phys. Rev. Lett. 2003, 90, 034101.

4. Zhang, X.; Zhu, T.; Zhang, S.; et al. Light-induced giant enhancement of nonreciprocal transport at KTaO₃-based interfaces. Nat. Commun. 2024, 15, 2992.

5. Li, C. N.; Liang, H. P.; Zhao, B. Q.; Wei, S. H.; Zhang, X. Machine learning assisted crystal structure prediction made simple. J. Mater. Inf. 2024, 4, 15.

6. Ji, W.; Wen, X. G. Categorical symmetry and noninvertible anomaly in symmetry-breaking and topological phase transitions. Phys. Rev. Res. 2020, 2, 033417.

7. Bender, C. M. Introduction to PT-symmetric quantum theory. Contemp. Phys. 2005, 46, 277-92.

8. Li, C.; Wang, R.; Zhang, S.; et al. Observation of giant non-reciprocal charge transport from quantum hall states in a topological insulator. Nat. Mater. 2024, 23, 1208-13.

9. Zhao, H. J.; Chen, P.; Paillard, C.; et al. Large spin splittings due to the orbital degree of freedom and spin textures in a ferroelectric nitride perovskite. Phys. Rev. B. 2020, 102, 041203.

10. Brunschwig, B. S.; Creutz, C.; Surin, N. Optical transitions of symmetrical mixed-valence systems in the class Ⅱ-Ⅲ transition regime. Chem. Soc. Rev. 2000, 31, 168-84.

11. Chen, Z.; Qiu, H.; Cheng, X.; et al. Defect-induced helicity dependent terahertz emission in Dirac semimetal PtTe₂ thin films. Nat. Commun. 2024, 15, 2605.

12. Niu, W.; Fang, Y. W.; Liu, R.; et al. Fully optical modulation of the two-dimensional electron gas at the γ-Al₂O₃/SrTiO₃ interface. J. Phys. Chem. Lett. 2022, 13, 2976-85.

13. Niu, W.; Zhang, Y.; Gan, Y.; et al. Giant tunability of the two-dimensional electron gas at the interface of γ-Al₂O₃/SrTiO₃γ-Al₂O₃/SrTiO₃. Nano. Lett. 2017, 17, 6878-85.

14. Hu, L.; Luo, Y.; Fang, Y.; et al. High thermoelectric performance through crystal symmetry enhancement in triply doped diamondoid compound Cu₂SnSe₃. Adv. Energy. Mater. 2021, 11, 2100661.

15. Hu, L.; Fang, Y. W.; Qin, F.; et al. High thermoelectric performance enabled by convergence of nested conduction bands in Pb₇Bi₄Se1₃ with low thermal conductivity. Nat. Commun. 2021, 12, 105.

16. Zheng, D.; Fang, Y. W.; Zhang, S.; et al. Berry phase engineering in SrRuO₃/SrIrO₃/SrTiO₃ superlattices induced by band structure reconstruction. ACS. Nano. 2021, 15, 5086-95.

17. Stormer, H. L. Nobel lecture: The fractional quantum hall effect. Rev. Mod. Phys. 1999, 71, 875-900.

18. Popovic, R. Hall-effect devices. Sens. Actuators. 1989, 17, 39-53.

19. Nagaosa, N.; Sinova, J.; Onoda, S.; MacDonald, A. H.; Ong, N. P. Anomalous hall effect. Rev. Mod. Phys. 2010, 82, 1539-92.

20. Sinova, J.; Valenzuela, S. O.; Wunderlich, J.; Back, C.; Jungwirth, T. Spin hall effects. Rev. Mod. Phys. 2015, 87, 1213-60.

21. Sodemann, I.; Fu, L. Quantum nonlinear hall effect induced by Berry curvature dipole in time-reversal invariant materials. Phys. Rev. Lett. 2015, 115, 216806.

22. Kang, K.; Li, T.; Sohn, E.; Shan, J.; Mak, R. F. Nonlinear anomalous hall effect in few-layer WTe₂. Nat. Mater. 2019, 18, 324-8.

23. Ma, Q.; Xu, S. Y.; Shen, H.; et al. Observation of the nonlinear hall effect under time-reversal-symmetric conditions. Nature 2019, 565, 337-42.

24. Tiwari, A.; Chen, F.; Zhong, S.; et al. Giant c-axis nonlinear anomalous hall effect in Td-MoTe₂ and WTe₂. Nat. Commun. 2021, 12, 2049.

25. Kumar, D.; Hsu, C. H.; Sharma, R.; et al. Room-temperature nonlinear hall effect and wireless radiofrequency rectification in Weyl semimetal TaIrTe₄. Nat. Nanotechnol. 2021, 16, 421-5.

26. Wang, N.; Kaplan, D.; Zhang, Z.; et al. Quantum-metric-induced nonlinear transport in a topological antiferromagnet. Nature 2023, 621, 487-92.

27. Gao, A.; Liu, Y. F.; Qiu, J. X.; et al. Quantum metric nonlinear hall effect in a topological antiferromagnetic heterostructure. Science 2023, 381, 181-6.

28. Rostami, H.; Juricic, V. Probing quantum criticality using nonlinear hall effect in a metallic Dirac system. Phys. Rev. Res. 2020, 2, 013069.

29. He, W. Y.; Law, K.T. Nonlinear hall effect in insulators. arxiv2024, 2411.07456. Available from: https://arxiv.org/abs/2411.07456 [Last accessed on 11 Apr 2024].

30. Lee, J. E.; Wang, A.; Chen, S.; et al. Spin-orbit-splitting-driven nonlinear hall effect in NbIrTe₄. Nat. Commun. 2024, 15, 3971.

31. Duan, S.; Qin, F.; Chen, P.; et al. Berry curvature dipole generation and helicity-to-spin conversion at symmetry-mismatched heterointerfaces. Nat. Nanotechnol. 2023, 18, 867-74.

32. He, Z.; Weng, H. Giant nonlinear hall effect in twisted bilayer WTe₂. NPJ. Quantum. Mater. 2021, 6, 101.

33. Hu, J. X.; Zhang, C. P.; Xie, Y. M.; Law, K. Nonlinear hall effects in strained twisted bilayer WSe₂. Commun. Phys. 2022, 5, 255.

34. Gao, A.; Liu, Y. F.; Hu, C.; et al. Layer hall effect in a 2D topological axion antiferromagnet. Nature 2021, 595, 521-5.

35. Du, Z.; Lu, H. Z.; Xie, X. Nonlinear hall effects. Nat. Rev. Phys. 2021, 3, 744-52.

36. Klitzing, K.; Dorda, G.; Pepper, M. New method for high-accuracy determination of the fine-structure constant based on quantized hall resistance. Phys. Rev. Lett. 1980, 45, 494-7.

37. Yasuda, K.; Wakatsuki, R.; Morimoto, T.; et al. Geometric hall effects in topological insulator heterostructures. Nat. Phys. 2016, 12, 555-9.

38. Gao, Y.; Yang, S. A.; Niu, Q. Field induced positional shift of Bloch electrons and its dynamical implications. Phys. Rev. Lett. 2014, 112, 166601.

39. Wang, C.; Gao, Y.; Xiao, D. Intrinsic nonlinear hall effect in antiferromagnetic tetragonal CuMnAs. Phys. Rev. Lett. 2021, 127, 277201.

40. Du, Z.; Wang, C.; Li, S.; et al. Disorder-induced nonlinear hall effect with time-reversal symmetry. Nat. Commun. 2019, 10, 3047.

41. Du, Z.; Wang, C.; Sun, H. P.; et al. Quantum theory of the nonlinear hall effect. Nat. Commun. 2021, 12, 5038.

42. Tokura, Y.; Nagaosa, N. Nonreciprocal responses from non-centrosymmetric quantum materials. Nat. Commun. 2018, 9, 3740.

43. Provost, J.; Vallee, G. Riemannian structure on manifolds of quantum states. Commun. Math. Phys. 1980, 76, 289-301.

44. Tsirkin, S.; Souza, I. On the separation of hall and ohmic nonlinear responses. SciPost. Phys. Core. 2022, 5, 039.

45. Holder, T.; Kaplan, D.; Yan, B. Consequences of time-reversal-symmetry breaking in the light-matter interaction: berry curvature, quantum metric, and diabatic motion. Phys. Rev. Res. 2020, 2, 033100.

46. Watanabe, H.; Yanase, Y. Nonlinear electric transport in odd-parity magnetic multipole systems: application to Mn-based compounds. Phys. Rev. Res. 2020, 2, 043081.

47. Isobe, H.; Xu, S. Y.; Fu, L. High-frequency rectification via chiral Bloch electrons. Sci. Adv. 2020, 6, eaay2497.

48. Liu, H.; Zhao, J.; Huang, Y. X.; et al. Intrinsic second-order anomalous hall effect and its application in compensated antiferromagnets. Phys. Rev. Lett. 2021, 127, 277202.

49. Han, J.; Uchimura, T.; Araki, Y.; et al. Room-temperature flexible manipulation of the quantum-metric structure in a topological chiral antiferromagnet. Nat. Phys. 2024, 20, 1110-7.

50. Berry, M. V. Quantal phase factors accompanying adiabatic changes. Proc. R. Soc. Lond. A. 1984, 392, 45-57.

51. Xiao, D.; Chang, M. C.; Niu, Q. Berry phase effects on electronic properties. Rev. Mod. Phys. 2010, 82, 1959-2007.

52. Bohm, A.; Mostafazadeh, A.; Koizumi, H.; Niu, Q.; Zwanziger, J. The Geometric phase in quantum systems: foundations, mathematical concepts, and applications in molecular and condensed matter physics. Springer Science & Business Media; 2013.

53. Karplus, R.; Luttinger, J. Hall effect in ferromagnetics. Phys. Rev. 1954, 95, 1154-60.

54. Low, T.; Jiang, Y.; Guinea, F. Topological currents in black phosphorus with broken inversion symmetry. Phys. Rev. B. 2015, 92, 235447.

55. Joseph, N. B.; Bandyopadhyay, A.; Narayan, A. Chirality-Tunable nonlinear hall effect. Chem. Mater. 2024, 36, 8602-12.

56. Zhu, H.; Yakobson, B. L. Creating chirality in the nearly two dimensions. Nat. Mater. 2024, 23, 316-22.

57. Peshchentseva, N.; Felser, C.; Zhang, Y. Quantized nonlinear hall effect from chiral monopole. Phys. Rev. B. 2024, 110, 155143.

58. Li, H.; Zhang, C.; Zhou, C.; et al. Quantum geometry quadrupole-induced third-order nonlinear transport in antiferromagnetic topological insulator MnBi₂Te₄. Nat. Commun. 2024, 15, 7779.

59. Sankar, S.; Liu, R.; Zhang, C. P.; et al. Experimental evidence for a berry curvature quadrupole in an antiferromagnet. Phys. Rev. X. 2024, 14, 021046.

60. Mak, K. F.; McGill, K. L.; Park, J.; McEuen, P. L. The valley hall effect in MoS₂ transistors. Science 2014, 344, 1489-92.

61. Xu, C.; Moore, J. E. Stability of the quantum spin hall effect: effects of interactions, disorder, and Z2 topology. Phys. Rev. B. 2006, 73, 045322.

62. Berger, L. Side-jump mechanism for the hall effect of ferromagnets. Phys. Rev. B. 1970, 2, 4559-66.

63. Smit, J. The spontaneous hall effect in ferromagnetics Ⅰ. Physica 1955, 21, 877-87.

64. Smit, J. The spontaneous hall effect in ferromagnetics Ⅱ. Physica 1958, 24, 39-51.

65. Cheng, B.; Gao, Y.; Zheng, Z.; et al. Giant nonlinear hall and wireless rectification effects at room temperature in the elemental semiconductor tellurium. Nat. Commun. 2024, 15, 5513.

66. Lu, X. F.; Zhang, C. P.; Wang, N.; et al. Nonlinear transport and radio frequency rectification in BiTeBr at room temperature. Nat. Commun. 2024, 15, 245.

67. He, P.; Isobe, H.; Zhu, D.; et al. Quantum frequency doubling in the topological insulator Bi₂Se₃. Nat. Commun. 2021, 12, 698.

68. Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; et al. Electric field effect in atomically thin carbon films. Science 2004, 306, 666-9.

69. Yang, H.; Valenzuela, S. O.; Chshiev, M.; et al. Two-dimensional materials prospects for non-volatile spintronic memories. Nature 2022, 606, 663-73.

70. Li, X.; Tao, L.; Chen, Z.; et al. Graphene and related two-dimensional materials: structure-property relationships for electronics and optoelectronics. Appl. Phys. Rev. 2017, 4, 021306.

71. Chia, X.; Pumera, M. Characteristics and performance of two-dimensional materials for electrocatalysis. Nat. Catal. 2018, 1, 909-21.

72. Zhang, Z.; Wang, N.; Cao, N.; et al. Controlled large non-reciprocal charge transport in an intrinsic magnetic topological insulator MnBi₂Te₄. Nat. Commun. 2022, 13, 6191.

73. Yasuda, K.; Morimoto, T.; Yoshimi, R.; et al. Large non-reciprocal charge transport mediated by quantum anomalous hall edge states. Nat. Nanotechnol. 2020, 15, 831-5.

74. Dean, C. R.; Wang, L.; Maher, P.; et al. Hofstadter's butterfly and the fractal quantum hall effect in moire superlattices. Nature 2013, 497, 598-602.

75. Novoselov, K. S.; Mishchenko, A.; Carvalho, A.; Castro Neto, A. 2D materials and van der Waals heterostructures. Science 2016, 353, aac9439.

76. Tong, Q.; Yu, H.; Zhu, Q.; et al. Topological mosaics in moire superlattices of van der Waals heterobilayers. Nat. Phys. 2017, 13, 356-62.

77. Finney, N. R.; Yankowitz, M.; Muraleetharan, L.; et al. Tunable crystal symmetry in graphene-boron nitride heterostructures with coexisting moire superlattices. Nat. Nanotechnol. 2019, 14, 1029-34.

78. Meng, K.; Li, Z.; Gao, Z.; et al. Gate-tunable berry curvature in van der Waals itinerant ferromagnetic CrTe. InfoMat 2024, 6, e12524.

79. Tian, Y.; Ye, L.; Jin, X. Proper scaling of the anomalous hall effect. Phys. Rev. Lett. 2009, 103, 087206.

80. Liu, E.; Sun, Y.; Kumar, N.; et al. Giant anomalous hall effect in a ferromagnetic kagome-lattice semimetal. Nat. Phys. 2018, 14, 1125-31.

81. Deng, Y.; Yu, Y.; Shi, M. Z.; et al. Quantum anomalous hall effect in intrinsic magnetic topological insulator MnBi₂Te₄. Science 2020, 367, 895-900.

82. Gao, A.; Chen, S. W.; Ghosh, B.; et al. An antiferromagnetic diode effect in even-layered MnBi₂Te₄. Nat. Electron. 2024, 7, 751-9.

83. He, P.; Koon, G. K. W.; Isobe, H.; et al. Graphene moire superlattices with giant quantum nonlinearity of chiral Bloch electrons. Nat. Nanotechnol. 2022, 17, 378-83.

84. Zhang, K. X.; Ju, H.; Kim, H.; et al. Broken inversion symmetry in van der Waals topological ferromagnetic metal iron germanium telluride. Adv. Mater. 2024, 36, 2312824.

85. Wang, S.; Li, X.; Zhang, H.; et al. Nonlinear Hall effect and scaling law in Sb-doped topological insulator MnBi₄Te₇. Appl. Phys. Lett. 2024, 124, 153102.

86. Lesne, E.; Saglam, Y. G.; Battilomo, R.; et al. Designing spin and orbital sources of Berry curvature at oxide interfaces. Nat. Mater. 2023, 22, 576-82.

87. Trama, M.; Cataudella, V.; Perroni, C.; Romeo, F.; Citro, R. Gate tunable anomalous hall effect: berry curvature probe at oxides interfaces. Phys. Rev. B. 2022, 106, 075430.

88. Groenendijk, D. J.; Autieri, C.; van Thiel, T. C.; et al. Berry phase engineering at oxide interfaces. Phys. Rev. Res. 2020, 2, 023404.

89. Yankowitz, M.; Ma, Q.; Jarillo-Herrero, P.; LeRoy, B. J. van der Waals heterostructures combining graphene and hexagonal boron nitride. Nat. Rev. Phys. 2019, 1, 112-25.

90. Li, Z.; Huang, J.; Zhou, L.; et al. An anisotropic van der Waals dielectric for symmetry engineering in functionalized heterointerfaces. Nat. Commun. 2023, 14, 5568.

91. Wang, L.; Meric, I.; Huang, P.; et al. One-dimensional electrical contact to a two-dimensional material. Science 2013, 342, 614-7.

92. Kinoshita, K.; Moriya, R.; Onodera, M.; et al. Dry release transfer of graphene and few-layer h-BN by utilizing thermoplasticity of polypropylene carbonate. npj. 2D. Mater. Appl. 2019, 3, 22.

93. Huang, M.; Wu, Z.; Zhang, X.; et al. Intrinsic nonlinear Hall effect and gate-switchable Berry curvature sliding in twisted bilayer graphene. Phys. Rev. Lett. 2023, 131, 066301.

94. Kim, K.; Yankowitz, M.; Fallahazad, B.; et al. van der Waals heterostructures with high accuracy rotational alignment. Nano. Lett. 2016, 16, 1989-95.

95. Saito, Y.; Ge, J.; Watanabe, K.; Taniguchi, T.; Young, A. F. Independent superconductors and correlated insulators in twisted bilayer graphene. Nat. Phys. 2020, 16, 926-30.

96. Tian, H.; Gao, X.; Zhang, Y.; et al. Evidence for Dirac flat band superconductivity enabled by quantum geometry. Nature 2023, 614, 440-4.

97. Park, J. M.; Cao, Y.; Watanabe, K.; Taniguchi, T.; Jarillo-Herrero, P. Tunable strongly coupled superconductivity in magic-angle twisted trilayer graphene. Nature 2021, 590, 249-55.

98. McGilly, L. J.; Kerelsky, A.; Finney, N. R.; et al. Visualization of moire superlattices. Nat. Nanotechnol. 2020, 15, 580-4.

99. Qiu, D.; Gong, C.; Wang, S.; et al. Recent advances in 2D superconductors. Adv. Mater. 2021, 33, 2006124.

100. Balents, L.; Dean, C. R.; Efetov, D. K.; Young, A. F. Superconductivity and strong correlations in moire flat bands. Nat. Phys. 2020, 16, 725-33.

101. Mak, K. F.; Shan, J. Semiconductor moire materials. Nat. Nanotechnol. 2022, 17, 686-95.

102. Xu, Y.; Liu, S.; Rhodes, D. A.; et al. Correlated insulating states at fractional fillings of moire superlattices. Nature 2020, 587, 211-8.

103. Huang, X.; Wang, T.; Miao, S.; et al. Correlated insulating states at fractional fillings of the WS₂/WSe₂ moire lattice. Nat. Phys. 2021, 17, 715-9.

104. Andrei, E. Y.; Efetov, D. K.; Jarillo-Herrero, P.; et al. The marvels of moire materials. Nat. Rev. Mater. 2021, 6, 201-6.

105. Ma, T.; Chen, H.; Yananosc, K.; et al. Growth of bilayer MoTe₂ single crystals with strong non-linear Hall effect. Nat. Commun. 2022, 13, 5465.

106. Min, L.; Tan, H.; Xie, Z.; et al. Strong room-temperature bulk nonlinear hall effect in a spin-valley locked Dirac material. Nat. Commun. 2023, 14, 364.

107. Suarez-Rodriguez, M.; Martin-Garcia, B.; Skowronski, W.; et al. Odd nonlinear conductivity under spatial inversion in chiral tellurium. Phys. Rev. Lett. 2021, 132, 046303.

108. Makushko, P.; Kovalev, S.; Zabila, Y.; et al. A tunable room-temperature nonlinear Hall effect in elemental bismuth thin films. Nat. Electron. 2024, 7, 207-15.

109. Wang, N.; You, J. Y.; Wang, A.; et al. Non-centrosymmetric topological phase probed by non-linear Hall effect. Natl. Sci. Rev. 2024, 11, nwa4103.

110. Qin, M. S.; Zhu, P. F.; Ye, X. G.; et al. Strain tunable Berry curvature dipole, orbital magnetization and nonlinear Hall effect in WSe₂ monolayer. Chin. Phys. Lett. 2021, 38, 017301.

111. Huang, M.; Wu, Z.; Hu, J.; et al. Giant nonlinear hall effect in twisted bilayer WSe₂. Natl. Sci. Rev. 2023, 10, nwac232.

112. Duan, J.; Jian, Y.; Gao, Y.; et al. Giant second-order nonlinear hall effect in twisted bilayer graphene. Phys. Rev. Lett. 2022, 129, 186801.

113. Sinha, S.; Adak, P. C.; Chakraborty, A.; et al. Berry curvature dipole senses topological transition in a moire superlattice. Nat. Phys. 2022, 18, 765-70.

114. Ye, X. G.; Zhu, P. F.; Xu, W. Z.; et al. Orbital polarization and third-order anomalous Hall effect in WTe₂. Phys. Rev. B. 2022, 106, 045414.

115. Lai, S.; Liu, H.; Zhang, Z.; et al. Third-order nonlinear Hall effect induced by the Berry-connection polarizability tensor. Nat. Nanotechnol. 2021, 16, 869-73.

116. Wang, C.; Xiao, R. C.; Liu, H.; et al. Room-temperature third-order nonlinear Hall effect in Weyl semimetal TaIrTe₄. Natl. Sci. Rev. 2022, 9, nwac020.

117. He, P.; Isobe, H.; Koon, G. K. W.; et al. Third-order nonlinear hall effect in a quantum Hall system. Nat. Nanotechnol. 2024, 19, 1460-5.

118. Chen, Z. H.; Liao, X.; Dong, J. W.; et al. Charge density wave modulated third-order nonlinear Hall effect in 1 T-VSe₂ nanosheets. Phys. Rev. B. 2024, 110, 235135.

119. Li, S.; Wang, X.; Yang, Z.; et al. Giant third-order nonlinear Hall effect in misfit layer compound (SnS)_1.17(NbS₂)₃. ACS. Appl. Mater. Interfaces. 2024, 16, 9.

120. Hamamoto, K.; Ezawa, M.; Kim, K. W.; Morimoto, T.; Nagaosa, N. Nonlinear spin current generation in noncentrosymmetric spin-orbit coupled systems. Phys. Rev. B. 2017, 95, 224430.

121. Araki, Y. Strain-induced nonlinear spin hall effect in topological Dirac semimetal. Sci. Rep. 2018, 8, 15236.

122. Zeng, C.; Nandy, S.; Taraphder, A.; Tewari, S. Nonlinear nernst effect in bilayer WTe₂. Phys. Rev. B. 2019, 100, 245102.

123. Zeng, C.; Nandy, S.; Tewari, S. Fundamental relations for anomalous thermoelectric transport coefficients in the nonlinear regime. Phys. Rev. Res. 2020, 2, 032066.

124. Nakai, R.; Nagaosa, N. Nonreciprocal thermal and thermoelectric transport of electrons in noncentrosymmetric crystals. Phys. Rev. B. 2019, 99, 115201.

125. Yu, X. Q.; Zhu, Z. G.; You, J. S.; Low, T.; Su, G. Topological nonlinear anomalous Nernst effect in strained transition metal dichalcogenides. Phys. Rev. B. 2019, 99, 201410.

126. Kumar, N.; Guin, S. N.; Felser, C.; Shekhar, C. Planar hall effect in the Weyl semimetal GdPtBi. Phys. Rev. B. 2018, 98, 041103.

127. Burkov, A. Giant planar Hall effect in topological metals. Phys. Rev. B. 2017, 96, 041110.

128. Tang, H.; Kawakami, R.; Awschalom, D.; Roukes, M. Giant planar Hall effect in epitaxial (Ga, Mn) as devices. Phys. Rev. Lett. 2003, 90, 107201.

129. He, P.; Zhang, S. S. L.; Zhu, D.; et al. Nonlinear planar Hall effect. Phys. Rev. Lett. 2019, 123, 016801.

130. Rao, W.; Zhou, Y. L.; Wu, Y. J.; Duan, H. J.; Deng, M. X.; et al. Theory for linear and nonlinear planar hall effect in topological insulator thin films. Phys. Rev. B. 2021, 103, 155415.

131. Xiao, J.; Wang, Y.; Wang, H.; et al. Berry curvature memory through electrically driven stacking transitions. Nat. Phys. 2020, 16, 1028-34.

132. Shao, D. F.; Zhang, S. H.; Gurung, G.; Yang, W.; Tsymbal, E. Y. Nonlinear anomalous hall effect for neel vector detection. Phys. Rev. Lett. 2020, 124, 067203.

133. Xiao, R. C.; Shao, D. F.; Zhang, Z. Q.; Jiang, H. Two-dimensional metals for piezoelectriclike devices based on Berry-curvature dipole. Phys. Rev. Appl. 2020, 13, 044014.

134. Zhang, Y.; Fu, L. Terahertz detection based on nonlinear hall effect without magnetic field. Proc. Natl. Acad. Sci. USA. 2021, 118, e2100736118.

135. Suarez-Rodriguez, M.; Martin-Garcia, B.; Skowronski, W.; et al. Microscale chiral rectennas for energy harvesting. Adv. Mater. 2024, 2400729.

136. Muhammad, S.; Tiang, J. J.; Wong, S. K.; et al. Harvesting systems for RF energy: trends, challenges, techniques, and tradeoffs. Electronics 2022, 11, 959.

137. Suarez-Rodriguez, M.; Juan, F. D.; Souza, I.; et al. Non-linear transport in non-centrosymmetric systems: from fundamentals to applications. arXiv2024, 2412.05253. Available from: https://arxiv.org/abs/2412.05253 [Last accessed on 11 Apr 2024].

138. Qin, F.; Shen, R.; Lee, C. H. Light-enhanced nonlinear hall effect. Commun. Phys. 2024, 7, 368.

139. Qin, F.; Shen, R.; Lee, C. H. Nonlinear Hall effects with an exceptional ring. arXiv2024, 2411.06509. Available from: http://dx.doi.org/10.48550/arXiv.2411.06509 [Last accessed on 11 Apr 2024].