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

Abstract

In recent years, it has 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 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, and the fourth-order NLAH voltage can be the leading response in the surface states of topological insulators induced by Berry curvature hexapoles. Our results are established by symmetry analysis, effective Hamiltonian and first-principles calculations. Other materials which support the higher-order NLAH effect are further proposed, including 2D antiferromagnets and ferromagnets, Weyl semimetals and twisted bilayer graphene near the quantum anomalous Hall phase.

17 pages, 5 figures

References in corpus (9)

• Quantum Anomalous Hall Effect in Hg${}_{1-y}$Mn${}_y$Te Quantum Wells
• Non-collinear Antiferromagnets and the Anomalous Hall Effect
• The Berry curvature dipole in Weyl semimetal materials: an ab initio study
• Band signatures for strong nonlinear Hall effect in bilayer WTe${}_2$
• Quantum Hall effect in a bulk antiferromagnet EuMnBi${}_2$ with magnetically confined two-dimensional Dirac fermions
• Quantum frequency doubling in the topological insulator Bi2Se3
• Berry Curvature Dipole in Strained Graphene: a Fermi Surface Warping Effect
• Berry connection polarizability tensor and third-order Hall effect
• Topological Nonlinear Anomalous Nersnt Effect in Strained Transition Metal Dichalcogenides

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• Quantum geometry quadrupole-induced third-order nonlinear transport in antiferromagnetic topological insulator MnBi2Te4
• Magnetic geometry induced quantum geometry and nonlinear transports
• An antiferromagnetic diode effect in even-layered MnBi2Te4
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• Quantum geometry encoded to pair potentials
• Signatures of hidden octupolar order from nonlinear Hall effects
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• Giant Third-Order Nonlinearity Induced by the Quantum Metric Quadrupole in Few-Layer WTe2
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• Emergent Phenomena with Broken Parity-Time Symmetry: Odd-order vs. Even-order Effects
• Intrinsic nonlinear Hall effect in two-dimensional honeycomb topological antiferromagnets
• Berry Curvature Spectroscopy from Bloch Oscillations
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• Roses in the Nonperturbative Current Response of Artificial Crystals
• Nonlinear anomalous transverse responses induced by Berry curvature quadrupole in systems with broken time-reversal symmetry
• Colossal Layer Nernst Effect in Twisted Moiré Layers
• Floquet-Bloch Theory for Nonperturbative Response to a Static Drive
• The "Sign problem" of the 3rd order anomalous Hall effect in topological magnetic materials
• Approximate half-integer quantization in anomalous planar transport in $d$-wave altermagnets
• Topological Kondo semimetals emulated in hetero-bilayer transition metal dichalcogenides
• Role of Disorder in Third-order Anomalous Hall Effect in Time-reversal Symmetric Systems
• Quantized crystalline-electromagnetic responses in insulators
• Charge transport in chiral solids as a possible tool in search of dark matter signals
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• Reconstructing the wavefunction of magnetic topological insulators MnBi2Te4 and MnBi4Te7 using spin-resolved photoemission
• Giant Room-Temperature Third-Order Electrical Transport in a Thin-Film Altermagnet Candidate
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• Strong Field Optical Hall Effect in 2D Weyl Semimetal
• Band Geometry Induced Third-Harmonic Generation
• Classification of spin Hall effect in two-dimensional systems
• Intrinsic nonlinear Hall effect beyond Bloch geometry
• Ferroelectric-tunable quantum nonlinearity of chiral Bloch electrons in a moiré system
• Identifying geometric third-order nonlinear transport in disordered materials
• Third-order nonlinear transport in a percolative two-dimensional superconductor
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• Quantum geometric map of magnetotransport