Nonlinear Hall Effects

Abstract

The Hall effects comprise one of the oldest but most vital fields in condensed matter physics, and they persistently inspire new findings, such as quantum Hall effects and topological phases of matter. The recently discovered nonlinear Hall effect is a new member of the family of Hall effects. It is characterized as a transverse Hall voltage in response to two longitudinal currents in the Hall measurement, but it does not require time-reversal symmetry to be broken. It has deep connections to symmetry and topology and, thus, opens new avenues by which to probe the spectral, symmetry and topological properties of emergent quantum materials and phases of matter. In this Perspective, we present an overview of the recent progress regarding the nonlinear Hall effect. We discuss the open problems, the prospects of the use of the nonlinear Hall effect in spectroscopic and device applications, and generalizations to other nonlinear transport effects.

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• Second-harmonic voltage responce for the magnetic Weyl semimetal Co${}_3$Sn${}_2$S${}_2$
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• Tutorial: Nonlinear magnonics
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• Revealing Quantum Geometry in Nonlinear Quantum Materials
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• Linear photogalvanic effect in surface states of topological insulators
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• Quantum Fluctuation of the Quantum Geometric Tensor and its Manifestation as Intrinsic Hall Signatures in Time-Reversal Invariant Systems
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• Crossed Nonlinear Dynamical Hall Effect in Twisted Bilayers
• Light-enhanced nonlinear Hall effect
• Quantum kinetic theory of quadratic responses
• Large nonlinear Hall effect and Berry curvature in KTaO3 based two-dimensional electron gas
• Nonlinear Hall effect induced by internal Coulomb interaction and phase relaxation process in a four-terminal system with time-reversal symmetry
• Extrinsic and Intrinsic Nonlinear Hall Effects across Berry-Dipole Transitions
• Quasi-symmetry Constrained Spin Ferromagnetism in Altermagnets
• Fundamental Distinction between Intrinsic and Extrinsic Nonlinear Thermal Hall Effects
• Quantum geometry encoded to pair potentials
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• Nonlinear magnetotransport in Weyl semimetal
• Rectification and nonlinear Hall effect by fluctuating finite-momentum Cooper pairs
• Quantum third-order nonlinear Hall effect of a four-terminal device with time-reversal symmetry
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• Nonlinear Hall effect on a disordered lattice
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• Topological and disorder corrections to the transverse Wiedemann-Franz law and Mott relation in kagome magnets
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• Nonlinear charge transport properties in chiral tellurium
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• Geometry-induced spin-filtering in photoemission maps from WTe${}_2$ surface states
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