Nonlinear Hall Effects in Strained Twisted Bilayer WSe$_2$

Hu, Jinxin; Zhang, Cheng-Ping; Xie, Ying-Ming; Law, Kam Tuen

doi:10.48550/arxiv.2004.14140

Cited by 11 publications

(26 citation statements)

References 26 publications

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“…The second term is the origin of the nonlinear Hall effect first pointed out by Sodemann and Fu [9] which has attracted many theoretical and experimental studies in recent years [10][11][12][13][19][20][21][22][23][24][25].…”

mentioning

confidence: 99%

“…This socalled nonlinear Hall effect is induced by the Berry curvature dipole, which is the first-order moment of the Berry curvature over occupied states. The nonlinear Hall effect has been observed experimentally in bilayer and multilayer WTe 2 [10,11] and more recently in twisted WSe 2 [12,13]. However, in principle, higher-order Berry curvature moments can be non-vanishing and their physical consequences are not known.…”

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confidence: 99%

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Higher-Order Nonlinear Anomalous Hall Effects Induced by Berry Curvature Multipoles

Zhang¹,

Gao²,

Xie³

et al. 2020

Preprint

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In recent years, it had been shown that Berry curvature monopoles and dipoles play essential roles in the anomalous Hall effect and the nonlinear Hall effect respectively. In this work, we demonstrate that Berry curvature multipoles (the higher moments of Berry curvatures at the Fermi energy) can induce higher-order nonlinear anomalous Hall (NLAH) effect. Specifically, an ac Hall voltage perpendicular to the current direction emerges, where the frequency is an integer multiple of the frequency of the applied current. Importantly, by analyzing the symmetry properties of all the 3D and 2D magnetic point groups, we note that the quadrupole, hexapole and even higher-order Berry curvature moments can cause the leading-order frequency multiplication in certain materials. To provide concrete examples, we point out that the third-order NLAH voltage can be the leading-order Hall response in certain antiferromagnets due to Berry curvature quadrupoles, while the fourth-order NLAH can be the leading response in the surface states of topological insulators induced by Berry curvature hexapole. Our results are established by symmetry analysis, effective Hamiltonian and first-principles calculations. Other materials that support the NLAH effect are further proposed, including 2D antiferromagnets and ferromagnets, Weyl semimetals and twisted bilayer graphene near the quantum anomalous Hall phase.

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confidence: 99%

mentioning

confidence: 99%

Higher-Order Nonlinear Anomalous Hall Effects Induced by Berry Curvature Multipoles

Zhang¹,

Gao²,

Xie³

et al. 2020

Preprint

Self Cite

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“…The time-reversal counterpart of the model makes an equal contribution to the nonlinear Hall effect. With the model, significant enhancement of the Berry curvature dipole is found near the band anticrossings, and the dipole changes sign when crossing the gap [19,23] and thus is highly tunable via strain engineering [59][60][61][62][63][64][65] and the twisted bilayer design [66][67][68][69].…”

Section: Theoretical Understandings a Geometric Nature Of Intrinsic Partmentioning

confidence: 97%

Nonlinear Hall Effects

Du,

Lu,

Xie

2021

Preprint

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“…Mathematically, the BCD is an integral of the product of local Berry curvature and velocity over the Fermi surface, so metals with prominent Berry curvature near the Fermi surface are ideal platforms to observe this effect. Under this guiding principle, as band degeneracies are natural sources of divergent Berry curvature, three-dimensional Weyl semimetals [21][22][23][24][25][26][27][28][29][30], two-dimensional transition-metal dichalcogenides [31][32][33][34][35][36][37][38][39][40][41], strained graphene [42][43][44] and topological insulators close to the phase boundary [45], which have either tilted gapless Weyl cones or tilted gapped Dirac cones, have been actively studied both theoretically and experimentally [46,47]. As the nonlinear Hall effect is an effect related to Fermi surface, it is noteworthy that doping is necessary for its observation in pristine gapped systems, such as topological insulators.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Hall effect in two-dimensional class AI metals

Liao,

Zhang,

Yan

2021

Preprint

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In a time-reversal invariant system, while the anomalous Hall effect identically vanishes in the linear response regime due to the constraint of time-reversal symmetry on the distribution of Berry curvature, a nonlinear Hall effect can emerge in the second-order response regime if the inversion symmetry is broken to allow a nonzero Berry curvature dipole (BCD) on the Fermi surface. In this work, we study the nonlinear Hall effect of the BCD origin in two-dimensional doped insulators and semimetals belonging to the symmetry class AI which has spinless time-reversal symmetry. Despite that the class AI does not host any strong topological insulator phase in two dimensions, we find that they can still be classified as topologically obstructed insulators and trivial insulators if putting certain constraint on the Hamiltonians. When the insulator gets closer to the phase boundary of the two distinct phases, we find that the BCDs will become more prominent if the doping level is located near the band edge. Moreover, when the insulator undergoes a phase transition between the two distinct phases, we find that the BCDs will dramatically change their signs. For the semimetals without inversion symmetry, we find that the BCDs will sharply reverse their signs when the doping level crosses the Dirac points. With the shift of the locations of Dirac points in energy, the critical doping level at which the BCDs sharply reverse their signs will accordingly change. Our study reveals that class AI materials can also have interesting geometrical and topological properties, and remarkable nonlinear Hall effect can also appear in this class of materials even though the spin-orbit coupling is negligible. Our findings broaden the scope of materials to study the nonlinear Hall effect and provide new perspectives for the application of this effect.

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Nonlinear Hall Effects in Strained Twisted Bilayer WSe$_2$

Cited by 11 publications

References 26 publications

Higher-Order Nonlinear Anomalous Hall Effects Induced by Berry Curvature Multipoles

Higher-Order Nonlinear Anomalous Hall Effects Induced by Berry Curvature Multipoles

Nonlinear Hall Effects

Nonlinear Hall effect in two-dimensional class AI metals

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