Disorder-induced nonlinear Hall effect with time-reversal symmetry

Abstract

The nonlinear Hall effect has opened the door towards deeper understanding of topological states of matter. It can be observed as the double-frequency Hall voltage response to an ac longitudinal current in the presence of time-reversal symmetry. Disorder plays indispensable roles in various linear Hall effects, such as the localization in the quantized Hall effects and the extrinsic mechanisms of the anomalous, spin, and valley Hall effects. Unlike in the linear Hall effects, disorder enters the nonlinear Hall effect even in the leading order. However, the disorder-induced contribution to the nonlinear Hall effect has not been addressed. Here, we derive the formulas of the nonlinear Hall conductivity in the presence of disorder scattering. We apply the formulas to calculate the nonlinear Hall response of the tilted 2D Dirac model, which is the symmetry-allowed minimal model for the nonlinear Hall effect and can serve as a building block in realistic band structures. More importantly, we construct the general scaling law of the nonlinear Hall effect, which may help in experiments to distinguish disorder-induced contributions to the nonlinear Hall effect. This work will be instructive for exploring unconventional responses upon breaking discrete or crystal symmetries in emergent physical systems and materials.

See source files for Supplemental Materials

References in corpus (19)

• Berry Phase Effects on Electronic Properties
• Anomalous Hall effect
• Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
• The Valley Hall Effect in MoS2 Transistors
• 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
• Proper Scaling of the Anomalous Hall Effect
• Semiclassical theories of the anomalous Hall effect
• Band signatures for strong nonlinear Hall effect in bilayer WTe${}_2$
• Anisotropic transport in the two-dimensional electron gas in the presence of spin-orbit coupling
• Berry curvature dipole current in transition metal dichalcogenides family
• Multivariable Scaling for the Anomalous Hall Effect
• 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
• Symmetry and Quantum Kinetics of the Non-linear Hall Effect
• Topological currents in black phosphorus with broken inversion symmetry
• Gyrotropic Hall effect in Berry-curved materials
• Highly tunable nonlinear Hall effects induced by spin-orbit couplings in strained polar transition-metal dichalcogenides
• The role of band-index-dependent transport relaxation times in anomalous Hall effect

Cited by in corpus (153)

• Nonlinear Hall Effects
• Quantum metric-induced nonlinear transport in a topological antiferromagnet
• Intrinsic nonlinear Hall effect in antiferromagnetic tetragonal CuMnAs
• Room temperature nonlinear Hall effect and wireless RF rectification in Weyl semimetal TaIrTe4
• Topology and geometry under the nonlinear electromagnetic spotlight
• Chiral photocurrent in parity-violating magnet and enhanced response in topological antiferromagnet
• Quantum theory of the nonlinear Hall effect
• Consequences of Time-reversal-symmetry Breaking in the Light-Matter Interaction: Berry Curvature, Quantum Metric and Diabatic Motion
• Transport in two-dimensional topological materials: recent developments in experiment and theory
• Unification of Nonlinear Anomalous Hall Effect and Nonreciprocal Magnetoresistance in Metals by the Quantum Geometry
• Symmetry and Quantum Kinetics of the Non-linear Hall Effect
• Quantum frequency doubling in the topological insulator Bi2Se3
• Zero-magnetic-field Hall effects in artificially corrugated bilayer graphene
• Quantum geometry induced nonlinear transport in altermagnets
• Giant spontaneous Hall effect in a nonmagnetic Weyl-Kondo semimetal
• Terahertz detection based on nonlinear Hall effect without magnetic field
• Theory of nonlinear Hall effects: renewed semiclassics from quantum kinetics
• Nonlinear Hall effect with time-reversal symmetry: Theory and material realizations
• Ferroelectric nonlinear anomalous Hall effect in few-layer WTe${}_2$
• Nonlinear Hall Acceleration and the Quantum Rectification Sum Rule
• Quantum geometry induced second harmonic generation
• Strain Tunable Berry Curvature Dipole, Orbital Magnetization and Nonlinear Hall Effect in WSe2 Monolayer
• Berry connection polarizability tensor and third-order Hall effect
• Difference frequency generation in topological semimetals
• Engineering Weyl phases and nonlinear Hall effects in T${}_d$-MoTe${}_2$
• 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
• Nonlinear transport in Weyl semimetals induced by Berry curvature dipole
• Roadmap for Photonics with 2D Materials
• Quantum geometry in condensed matter
• Tunable large Berry dipole in strained twisted bilayer graphene
• Intrinsic Nonlinear Spin Magnetoelectricity in Centrosymmetric Magnets
• Strong Room-Temperature Bulk Nonlinear Hall Effect in a Spin-Valley Locked Dirac Material
• Highly tunable nonlinear Hall effects induced by spin-orbit couplings in strained polar transition-metal dichalcogenides
• Designing spin and orbital sources of Berry curvature at oxide interfaces
• Control over Berry Curvature Dipole with Electric Field in WTe2
• Magnus Hall Effect
• Intrinsic nonlinear Hall effect and gate-switchable Berry curvature sliding in twisted bilayer graphene
• Nonlinear Hall effect in Weyl semimetals induced by chiral anomaly
• Effects of renormalization and non-Hermiticity on nonlinear responses in strongly-correlated electron systems
• Non-linear Nernst effect in bilayer WTe${}_2$
• Nonlinear anomalous Hall effects probe topological phase-transitions in twisted double bilayer graphene
• Resonant photovoltaic effect in doped magnetic semiconductors
• Orbital Origin of Intrinsic Planar Hall Effect
• Time-Reversal-Even Nonlinear Current Induced Spin Polarization
• Intrinsic Nonlinear Hall Detection of the Néel Vector for Two-Dimensional Antiferromagnetic Spintronics
• Nonlinear Valley Hall Effect
• Anomalous skew-scattering nonlinear Hall effect and chiral photocurrents in {\it PT}-symmetric antiferromagnets
• Dissipation and geometry in nonlinear quantum transports of multiband electronic systems
• Third-order and fifth-order nonlinear spin-current generation in $g$-wave and $i$-wave altermagnets, and perfectly nonreciprocal spin-current in $f$-wave magnets
• Revealing Quantum Geometry in Nonlinear Quantum Materials
• Non-linear Hall Effects: Mechanisms and Materials
• Fundamental relations for anomalous thermoelectric transport coefficients in the non-linear regime
• Orbital angular momentum of Bloch electrons: equilibrium formulation, magneto-electric phenomena, and the orbital Hall effect
• Enhanced anomalous Nernst effect in disordered Dirac and Weyl materials
• Semiclassical theory of the circular photogalvanic effect in gyrotropic systems
• Unconventional Hall Effect induced by Berry Curvature
• Electrical Detection of Ferroelectric-like Metals through Nonlinear Hall Effect
• On the separation of Hall and Ohmic nonlinear responses
• Gate-Tunable Berry Curvature Dipole Polarizability in Dirac Semimetal Cd3As2
• Odd non-linear conductivity under spatial inversion in chiral Tellurium
• The quantum metric of electrons with spin-momentum locking
• Scaling parameters in anomalous and nonlinear Hall effects depend on temperature
• Non-linear transport without spin-orbit coupling or warping in two-dimensional Dirac semimetals
• Observation of Nonlinear Spin-Charge Conversion in the Thin Film of Nominally Centrosymmetric Dirac Semimetal SrIrO3 at Room Temperature
• Quantum kinetic theory of nonlinear thermal current
• Third-order Hall effect in the surface states of a topological insulator
• Berry curvature induced nonlinear magnetoresistivity in two dimensional systems
• Infinite Berry Curvature of Weyl Fermi Arcs
• Scaling Law for Time-Reversal-Odd Nonlinear Transport
• Magnetic geometry induced quantum geometry and nonlinear transports
• Intrinsic nonlinear thermal Hall transport of magnons: A Quantum kinetic theory approach
• 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
• Quantum Hall effect originated from helical edge states in Cd${}_3$As${}_2$
• Quantum Fluctuation of the Quantum Geometric Tensor and its Manifestation as Intrinsic Hall Signatures in Time-Reversal Invariant Systems
• Equivalence of semiclassical and response theories for second-order nonlinear ac Hall effects
• Ferroic Berry Curvature Dipole in a Topological Crystalline Insulator at Room Temperature
• Orbital design of Berry curvature: pinch points and giant dipoles induced by crystal fields
• Crossed Nonlinear Dynamical Hall Effect in Twisted Bilayers
• Observation of nonlinear planar Hall effect in magnetic insulator/topological insulator heterostructures
• Light-enhanced nonlinear Hall effect
• Quantum kinetic theory of quadratic responses
• Theory of Nonlinear Response for Charge and Spin Currents
• Nonlinear Hall effect induced by internal Coulomb interaction and phase relaxation process in a four-terminal system with time-reversal symmetry
• Nonlinear Landauer formula: Nonlinear response theory of disordered and topological materials
• Fundamental Distinction between Intrinsic and Extrinsic Nonlinear Thermal Hall Effects
• Non-Linear Hall Effect in Multi-Weyl Semimetals
• Gate-dependent non-linear Hall effect at room temperature in topological semimetal GeTe
• Quantum third-order nonlinear Hall effect of a four-terminal device with time-reversal symmetry
• Observation of time-reversal symmetric Hall effect in graphene-WSe2 heterostructures at room temperature
• Nonlinear Hall effect on a disordered lattice
• High laser harmonics induced by the Berry curvature in time-reversal invariant materials
• Topological and disorder corrections to the transverse Wiedemann-Franz law and Mott relation in kagome magnets
• Nonlinear Hall effect in two-dimensional class AI metals
• Detecting Lifshitz Transitions Using Nonlinear Conductivity in Bilayer Graphene
• Intrinsic gyrotropic magnetic current from Zeeman quantum geometry
• Unidirectional valley-contrasting photo-current in strained transition metal dichalcogenide monolayers
• Nonlinear electrical transport unveils Fermi surface malleability in a moiré heterostructure
• 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
• Symmetry Origin and Microscopic Mechanism of Electrical Magnetochiral Anisotropy in Tellurium
• Nonlinear Hall effect and scaling law in Sb-doped topological insulator MnBi4Te7
• Detection of quantum geometric tensor by nonlinear optical response
• Non-adiabatic Hall effect at Berry curvature hot spot
• Thermal difference reflectivity of tilted 2D Dirac materials
• Electric field induced second-order anomalous Hall transport in unconventional Rashba systems
• Room-temperature nonlinear transport and microwave rectification in antiferromagnetic MnBi${}_2$Te${}_4$ films
• Charge density wave modulated third-order nonlinear Hall effect in 1$T$-VSe${}_2$ nanosheets
• Electrical control of intrinsic nonlinear Hall effect in antiferromagnetic topological insulator sandwiches
• A Clarification on Quantum-Metric-Induced Nonlinear Transport
• How to identify and characterize strongly correlated topological semimetals
• Intrinsic nonlinear Nernst and Seebeck effect
• Proper Definition of Intrinsic Nonlinear Current
• Second-harmonic response as a tool to detect spin textures in magnetic nodal-line semimetal Fe${}_3$GeTe${}_2$
• Nonlinear Hall effects with an exceptional ring
• Quantum geometric moment encodes stacking order of moiré matter
• Geometrical Nonlinear Hall Effect Induced by Lorentz Force
• Nonlinear and nonreciprocal transport effects in untwinned thin films of ferromagnetic Weyl metal SrRuO${}_3$
• Second-harmonic voltage responce for the magnetic Weyl semimetal Co${}_3$Sn${}_2$S${}_2$
• Quantum Nonlinear Acoustic Hall Effect and Inverse Acoustic Faraday Effect in Dirac Insulators
• Emergent Topological Semimetal
• Magnetic Field Induced Quantum Metric Dipole in Dirac Semimetal Cd3As2
• Orbital anomalous Hall effect in the few-layer Weyl semimetal TaIrTe4
• Role of Disorder in Third-order Anomalous Hall Effect in Time-reversal Symmetric Systems
• Nonlinear Hall response in the driving dynamics of ultracold atoms in optical lattices
• Nonlinear planar magnetotransport as a probe of the topology of surface states
• Nonlinear Valley and Spin Valves in Bilayer Graphene
• Quadrupolar photovoltaic effect in the terahertz range in a two-dimensional spin-3/2 hole system
• Microscopic Theory of Nonlinear Hall Effect in Three-dimensional Magnetic Systems
• Nonlinear Hall effect driven by spin-charge-coupled motive force
• Circular Photon Drag Effect in Dirac electrons by Quantum Geometry
• Second-Order Conductivity Probes a Cascade of Singularities in a Moiré Superlattice
• Nonlinear edge transport in a quantum Hall system
• General method for calculating transport properties of disordered mesoscopic systems based on the nonequilibrium Green's function formalism
• Probing quantum geometric nonlinear magnetization via second-harmonic magneto-optical Kerr effect
• Band Geometry Induced Third-Harmonic Generation
• Orbital magnetization as the origin of the nonlinear Hall effect
• Sign reversal of magnetoresistivity in massive nodal-line semimetals due to Lifshitz transition of Fermi surface
• Real Space Characterization of Nonlinear Hall Effect in Confined Directions
• Fourth-order and six-order nonlinear spin current rectifier in three-dimensional $h$-wave and $j$-wave odd-parity magnet
• Quantum geometric magnetic monopole and two-phase superconductivity in CeRh${}_2$As${}_2$
• Topological bands in metals
• Identifying geometric third-order nonlinear transport in disordered materials
• Emerging nonlinear Hall effect in Kane-Mele two-dimensional topological insulators
• Quantum theory of nonlinear electromagnetic response
• Quantum Christoffel Nonlinear Magnetization
• Revealing the non-adiabatic and non-Abelian multiple-band effects via anisotropic valley Hall conduction in bilayer graphene
• Resonant Nonlinear Hall Effect in Two-Dimensional Electron Systems
• Disorder-mediated linear and nonlinear magnetotransport in the charge-density-wave material $\mathrm{T}{\mathrm{a}}_2\mathrm{NiS}{\mathrm{e}}_7$
• Prediction of a layer nonlinear Hall effect in bilayer nonmagnetic or antiferromagnetic systems