Theory of nonlinear Hall effects: renewed semiclassics from quantum kinetics

Abstract

We propose a modified Boltzmann nonlinear electric-transport framework which differs from the nonlinear generalization of the linear Boltzmann formalism by a contribution that has no counterpart in linear response. This contribution follows from the interband-coherence effect of dc electric-fields during scattering and is related to the interband Berry connection. As an application, we demonstrate it in the second-order nonlinear Hall effect of the tilted massive Dirac model. The intuitive Boltzmann constructions are confirmed by a quantum kinetic theory, which shows that arbitrary $n$th-order nonlinear dc response up to the first three leading contributions in the weak disorder potential is handled by the same few gauge-invariant semiclassical ingredients.

arXiv comment2 figures, 1 table; Extended version. A section detailing the differences between our theory and other existing ones on the nonlinear Hall effect is added in response to a referee's report

References in corpus (30)

• Anomalous Hall effect
• Quantum nonlinear Hall effect induced by Berry curvature dipole in time-reversal invariant materials
• Observation of the nonlinear Hall effect under time reversal symmetric conditions
• Topological nature of nonlinear optical effects in solids
• Giant anisotropic nonlinear optical response in transition metal monopnictide Weyl semimetals
• Field Induced Positional Shift of Bloch Electrons and its Dynamical Implications
• Electrically switchable Berry curvature dipole in the monolayer topological insulator WTe2
• Semiclassical theories of the anomalous Hall effect
• Anomalous Hall effect in 2D Dirac band: link between Kubo-Streda formula and semiclassical Boltzmann equation approach
• Disorder-induced nonlinear Hall effect with time-reversal symmetry
• Confinement-induced Berry phase and helicity-dependent photocurrents
• The Berry curvature dipole in Weyl semimetal materials: an ab initio study
• Diagrammatic approach to nonlinear optical response with application to Weyl semimetals
• Band signatures for strong nonlinear Hall effect in bilayer WTe${}_2$
• Semiclassical theory of nonlinear magneto-optical responses with applications to topological Dirac/Weyl semimetals
• Berry curvature dipole current in transition metal dichalcogenides family
• Gyrotropic effects in trigonal tellurium studied from first principles
• Strongly enhanced Berry dipole at topological phase transitions in BiTeI
• Electrically tuneable nonlinear anomalous Hall effect in two-dimensional transition-metal dichalcogenides WTe2 and MoTe2
• Coordinate shift in the semiclassical Boltzmann equation and the anomalous Hall effect
• Topological currents in black phosphorus with broken inversion symmetry
• Inter-band Coherence Response to Electric Fields in Crystals
• Gyrotropic Hall effect in Berry-curved materials
• Anomalous Hall effect with massive Dirac fermions
• Direct current driven by ac electric field in quantum wells
• Semiclassical theory of spin-orbit torques in disordered multiband electron systems
• Orbital mechanism of the circular photogalvanic effect in quantum wells
• The role of band-index-dependent transport relaxation times in anomalous Hall effect
• Semiclassical Boltzmann theory of spin Hall effects in giant Rashba systems
• Boltzmann approach to spin-orbit-induced transport in effective quantum theories

Cited by in corpus (76)

• Nonlinear Hall Effects
• Intrinsic nonlinear Hall effect in antiferromagnetic tetragonal CuMnAs
• Topology and geometry under the nonlinear electromagnetic spotlight
• Quantum theory of the nonlinear Hall effect
• Zero-magnetic-field Hall effects in artificially corrugated bilayer graphene
• Terahertz detection based on nonlinear Hall effect without magnetic field
• Nonlinear Hall effect with time-reversal symmetry: Theory and material realizations
• Nonlinear Hall Acceleration and the Quantum Rectification Sum Rule
• Strain Tunable Berry Curvature Dipole, Orbital Magnetization and Nonlinear Hall Effect in WSe2 Monolayer
• Berry connection polarizability tensor and third-order Hall effect
• Nonlinear electric transport in odd-parity magnetic multipole systems: Application to Mn-based compounds
• Higher-Order Nonlinear Anomalous Hall Effects Induced by Berry Curvature Multipoles
• Orbital Magneto-Nonlinear Anomalous Hall Effect in Kagome Magnet Fe${}_3$Sn${}_2$
• Non-linear Nernst effect in bilayer WTe${}_2$
• Resonant photovoltaic effect in doped magnetic semiconductors
• Tunable room temperature nonlinear Hall effect from the surfaces of elementary bismuth thin films
• Time-Reversal-Even Nonlinear Current Induced Spin Polarization
• Magnus Nernst and thermal Hall effect
• Anomalous skew-scattering nonlinear Hall effect and chiral photocurrents in {\it PT}-symmetric antiferromagnets
• Twisted photovoltaics at terahertz frequencies from momentum shift current
• Nonreciprocal Landau-Zener tunneling
• Revealing Quantum Geometry in Nonlinear Quantum Materials
• Nonlinear nonreciprocal transport in antiferromagnets free from spin-orbit coupling
• Unifying semiclassics and quantum perturbation theory at nonlinear order
• Semiclassical theory of the circular photogalvanic effect in gyrotropic systems
• Electrical Detection of Ferroelectric-like Metals through Nonlinear Hall Effect
• Conserved current of nonconserved quantities
• Quantum Kinetic Theory of Nonlinear Optical Currents: Finite Fermi surface and Fermi sea contributions
• Non-linear transport without spin-orbit coupling or warping in two-dimensional Dirac semimetals
• Berry curvature induced nonlinear magnetoresistivity in two dimensional systems
• Infinite Berry Curvature of Weyl Fermi Arcs
• Quantum Kinetic Theory of Thermoelectric and Thermal Transport in a Magnetic Field
• Spontaneous Crystal Thermal Hall Effect in Insulating Altermagnets
• Scaling Law for Time-Reversal-Odd Nonlinear Transport
• Intrinsic nonlinear thermal Hall transport of magnons: A Quantum kinetic theory approach
• First Principles Calculation of Ballistic Current from Electron-Hole Interaction
• Equivalence of semiclassical and response theories for second-order nonlinear ac Hall effects
• Disorder in the non-linear anomalous Hall effect of $\mathcal{P}\mathcal{T}$-symmetric Dirac fermions
• Ferroic Berry Curvature Dipole in a Topological Crystalline Insulator at Room Temperature
• Observation of nonlinear planar Hall effect in magnetic insulator/topological insulator heterostructures
• Quantum kinetics of anomalous and nonlinear Hall effects in topological semimetals
• Quantum kinetic theory of quadratic responses
• Quantum nonlinear planar Hall effect in bilayer graphene: an orbital effect of a steady in-plane magnetic field
• Extrinsic and Intrinsic Nonlinear Hall Effects across Berry-Dipole Transitions
• Nonlinear Landauer formula: Nonlinear response theory of disordered and topological materials
• Non-Linear Hall Effect in Multi-Weyl Semimetals
• High laser harmonics induced by the Berry curvature in time-reversal invariant materials
• Nonlinear Hall effect on a disordered lattice
• Charge Conservation Beyond Uniformity: Spatially Inhomogeneous Electromagnetic Response in Periodic Solids
• Nonlinear Hall effect in two-dimensional class AI metals
• Planar Hall Plateau in Magnetic Weyl Semimetals
• Magnetic parity violation and parity-time-reversal-symmetric magnets
• Nonlinear magnetotransport in a two-dimensional system with merging Dirac points
• Polarization and third-order Hall effect in III-V semiconductor heterojunctions
• Intrinsic nonlinear Hall effect in two-dimensional honeycomb topological antiferromagnets
• Non-adiabatic Hall effect at Berry curvature hot spot
• Detection of quantum geometric tensor by nonlinear optical response
• 3D Topological Plasmons in Weyl Semimetals
• Electrical control of intrinsic nonlinear Hall effect in antiferromagnetic topological insulator sandwiches
• Theory of wavepacket transport under narrow gaps and spatial textures: non-adiabaticity and semiclassicality
• Second-harmonic response as a tool to detect spin textures in magnetic nodal-line semimetal Fe${}_3$GeTe${}_2$
• Proper Definition of Intrinsic Nonlinear Current
• Enhanced nonlinear Hall effect by Cooper pairs near superconductor criticality
• Nonlinear Hall effects with an exceptional ring
• Quantum Geometric Origin of the Intrinsic Nonlinear Hall Effect
• Second-harmonic voltage responce for the magnetic Weyl semimetal Co${}_3$Sn${}_2$S${}_2$
• Magnetic instability under ferroaxial moment
• Microscopic Theory of Nonlinear Hall Effect in Three-dimensional Magnetic Systems
• Boltzmann electronic dc transport in multiorbital weakly-disordered crystals
• Band Geometry Induced Third-Harmonic Generation
• Energy magnetization and transport in systems with a non-zero Berry curvature in a magnetic field
• Resonant Nonlinear Hall Effect in Two-Dimensional Electron Systems
• Intraband circular photogalvanic effect in Weyl semimetals
• Identifying geometric third-order nonlinear transport in disordered materials
• Prediction of a layer nonlinear Hall effect in bilayer nonmagnetic or antiferromagnetic systems
• Emerging nonlinear Hall effect in Kane-Mele two-dimensional topological insulators