Quantum theory of the nonlinear Hall effect

Abstract

The nonlinear Hall effect is an unconventional response, in which a voltage can be driven by two perpendicular currents in the Hall-bar measurement. Unprecedented in the family of the Hall effects, it can survive time-reversal symmetry but is sensitive to the breaking of discrete and crystal symmetries. It is a quantum transport phenomenon that has deep connection with the Berry curvature. However, a full quantum description is still absent. Here we construct a quantum theory of the nonlinear Hall effect by using the diagrammatic technique. Quite different from nonlinear optics, nearly all the diagrams account for the disorder effects, which play decisive role in the electronic transport. After including the disorder contributions in terms of the Feynman diagrams, the total nonlinear Hall conductivity is enhanced but its sign remains unchanged for the 2D tilted Dirac model, compared to the one with only the Berry curvature contribution. We discuss the symmetry of the nonlinear conductivity tensor and predict a pure disorder-induced nonlinear Hall effect for point groups $C_3$, $C_{3h}$, $C_{3v}$, $D_{3h}$, $D_3$ in 2D, and $T$, $T_d$, $C_{3h}$, $D_{3h}$ in 3D. This work will be helpful for explorations of the topological physics beyond the linear regime.

9 pages, 3 figures, 1 table. The highlighted tensor elements in Table I can be found here

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• Giant nonlinear Hall effect in twisted WSe${}_2$
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• Orbital Magneto-Nonlinear Anomalous Hall Effect in Kagome Magnet Fe${}_3$Sn${}_2$
• Nonlinear magnon spin Nernst effect in antiferromagnets and strain-tunable pure spin current
• Intrinsic nonlinear Hall effect and gate-switchable Berry curvature sliding in twisted bilayer graphene
• Dissipation and geometry in nonlinear quantum transports of multiband electronic systems
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• Non-linear Hall Effects: Mechanisms and Materials
• Unifying semiclassics and quantum perturbation theory at nonlinear order
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• Berry curvature induced nonlinear magnetoresistivity in two dimensional systems
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• Magnetic geometry induced quantum geometry and nonlinear transports
• Interaction-Enhanced Topological Hall Effects in Strained Twisted Bilayer Graphene
• Topological Magnus responses in two and three dimensional systems
• Disorder in the non-linear anomalous Hall effect of $\mathcal{P}\mathcal{T}$-symmetric Dirac fermions
• Discovery of a magnetic Dirac system with large intrinsic non-linear Hall effect
• Quantum kinetic theory of quadratic responses
• Nonlinear Quantum Electrodynamics in Dirac materials
• Nonlinear Landauer formula: Nonlinear response theory of disordered and topological materials
• PYATB: An Efficient Python Package for Electronic Structure Calculations Using Ab Initio Tight-Binding Model
• Nonlinear Hall effect induced by internal Coulomb interaction and phase relaxation process in a four-terminal system with time-reversal symmetry
• Non-Linear Hall Effect in Multi-Weyl Semimetals
• Fundamental Distinction between Intrinsic and Extrinsic Nonlinear Thermal Hall Effects
• Quantum third-order nonlinear Hall effect of a four-terminal device with time-reversal symmetry
• Gate-dependent non-linear Hall effect at room temperature in topological semimetal GeTe
• Nonlinear Hall effect on a disordered lattice
• Nonlinear charge transport properties in chiral tellurium
• Second Harmonic Helicity and Faraday Rotation in Gated Single-Layer 1T${}^{\prime }$-WTe${}_2$
• Nonlinear magnetotransport in a two-dimensional system with merging Dirac points
• Nonlinear Hall effect from long-lived valley-polarizing relaxons
• Nonlinear electrical transport unveils Fermi surface malleability in a moiré heterostructure
• Magnetic parity violation and parity-time-reversal-symmetric magnets
• Polarization and third-order Hall effect in III-V semiconductor heterojunctions
• Symmetry Origin and Microscopic Mechanism of Electrical Magnetochiral Anisotropy in Tellurium
• Switchable in-plane anomalous Hall effect by magnetization orientation in monolayer ${\mathrm{Mn}}_3{\mathrm{Si}}_2{\mathrm{Te}}_6$
• Terahertz radiation driven nonlinear transport phenomena in two-dimensional tellurene
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• Nonlinear charge and thermal transport properties induced by orbital magnetic moment in chiral crystal cobalt monosilicide
• Nonlinear Edelstein Effect in Strongly Correlated Electron Systems
• Interband contributions to nonlinear transport in semiconductor nanostructures
• Nonlinear Hall effects with an exceptional ring
• Enhanced nonlinear Hall effect by Cooper pairs near superconductor criticality
• Quantum unidirectional magnetoresistance
• Geometrical Nonlinear Hall Effect Induced by Lorentz Force
• Proximity-induced nonlinear magnetoresistances on topological insulators
• Quantum Geometric Origin of the Intrinsic Nonlinear Hall Effect
• Moiré amplification of highly tunable shift current response in twisted trilayer graphene
• Role of Disorder in Third-order Anomalous Hall Effect in Time-reversal Symmetric Systems
• Nonlinear Spectroscopy via Generalized Quantum Phase Estimation
• Microscopic Theory of Nonlinear Hall Effect in Three-dimensional Magnetic Systems
• Quantum Geometric Origin of Orbital Magnetization
• Magneto-nonlinear Hall effect in time-reversal breaking system
• Real Space Characterization of Nonlinear Hall Effect in Confined Directions
• Superfluid Stiffness and Josephson Quantum Capacitance: Adiabatic Approach and Topological Effects
• Orbital magnetization as the origin of the nonlinear Hall effect
• Band Geometry Induced Third-Harmonic Generation
• General method for calculating transport properties of disordered mesoscopic systems based on the nonequilibrium Green's function formalism
• Quantum theory of nonlinear electromagnetic response
• Weak localization and antilocalization corrections to nonlinear transport: a semiclassical Boltzmann treatment
• Identifying geometric third-order nonlinear transport in disordered materials
• Dissipation-Shaped Quantum Geometry in Nonlinear Transport
• Evidence of Spin-Valley Coupling in Dirac Material BaMnBi2 Probed by Quantum Hall Effect and Nonlinear Hall Effect
• Emerging nonlinear Hall effect in Kane-Mele two-dimensional topological insulators
• Evolution of the Berry curvature dipole in uniaxially strained bilayer graphene
• Lattice-induced wavefunction effects on trapped superfluids
• Resonant Nonlinear Hall Effect in Two-Dimensional Electron Systems
• Prediction of a layer nonlinear Hall effect in bilayer nonmagnetic or antiferromagnetic systems