Quantum nonlinear Hall effect induced by Berry curvature dipole in time-reversal invariant materials

Abstract

It is well-known that a non-vanishing Hall conductivity requires time-reversal symmetry breaking. However, in this work, we demonstrate that a Hall-like transverse current can occur in second-order response to an external electric field in a wide class of time-reversal invariant and inversion breaking materials, at both zero and twice the optical frequency. This nonlinear Hall effect has a quantum origin arising from the dipole moment of the Berry curvature in momentum space, which generates a net anomalous velocity when the system is in a current-carrying state. We show that the nonlinear Hall coefficient is a rank-two pseudo-tensor, whose form is determined by point group symmetry. We discus optimal conditions to observe this effect and propose candidate two- and three-dimensional materials, including topological crystalline insulators, transition metal dichalcogenides and Weyl semimetals.

5 pages, 1 figure

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• Hybrid skyrmion and anti-skyrmion phases in polar $C_{4v}$ systems
• Toroidal Scattering and Nonreciprocal Transport by Magnetic Impurities
• Geometrical Nonlinear Hall Effect Induced by Lorentz Force
• Quantum geometry and $X$-wave magnets with $X=p,d,f,g,i$
• Quantum geometric moment encodes stacking order of moiré matter
• Enhanced nonlinear Hall effect by Cooper pairs near superconductor criticality
• Nonlinear Hall effects with an exceptional ring
• Interband contributions to nonlinear transport in semiconductor nanostructures
• Proper Definition of Intrinsic Nonlinear Current
• Intrinsic Orbital Origin for the Chirality-Dependent Nonlinear Planar Hall Effect of Topological Nodal Fermions in Chiral Crystals
• Phase shifts, band geometry and responses in triple-Q charge and spin density waves
• Nonlinear anomalous transverse responses induced by Berry curvature quadrupole in systems with broken time-reversal symmetry
• Orbital magnetization senses the topological phase transition in a spin-orbit coupled $\alpha$-$T_3$ system
• Nonlinear and nonreciprocal transport effects in untwinned thin films of ferromagnetic Weyl metal SrRuO${}_3$
• Orbital Gravito-Magnetoelectric response and Orbital magnetic quadrupole moment correction
• Current-induced quasiparticle magnetic multipole moments
• Second-harmonic response as a tool to detect spin textures in magnetic nodal-line semimetal Fe${}_3$GeTe${}_2$
• Engineering spin-orbit effects and Berry curvature by deposition of Eu on WSe${}_2$
• Chirality-dependent second-order spin current in systems with time-reversal symmetry
• Semiclassical transport with Berry curvature: Chambers formula and applications to systems with Fermi surface topological transitions
• Nonlinear thermoelectric probes of anomalous electron lifetimes in topological Fermi liquids
• Direct current in a stirred optical lattice
• Movable Dirac Points with Ferroelectrics: Kink States and Berry Curvature Dipoles
• Realizing a topological diode effect on the surface of a topological Kondo insulator
• Bloch theorem dictated wave chaos in microcavity crystals
• Nonlinear chiral photocurrent in parity-violating magnetic Weyl semimetals
• Nonlinear Hall Effect in Antiferromagnetic Half-Heusler Materials
• Supercurrent-induced Anomalous Thermal Hall Effect as a New Probe to Superconducting Gap Anisotropy
• Electrical magnetochiral anisotropy and quantum metric in chiral conductors
• Inducing Berry Curvature Dipole in Multilayer Graphene through Inhomogeneous Interlayer Sliding
• Interaction-induced nonlinear magnon transport in noncentrosymmetric magnets
• Quantum Geometric Origin of the Intrinsic Nonlinear Hall Effect
• Engineering nonlinear Hall effect in bilayer graphene/black phosphorus heterostructures
• Phonon-limited carrier transport in the Weyl semimetal TaAs
• Proximity-induced nonlinear magnetoresistances on topological insulators
• Twistronics and moiré superlattice physics in 2D transition metal dichalcogenides
• Local Probes for Quantum Hall Ferroelectrics and Nematics
• Second-harmonic voltage responce for the magnetic Weyl semimetal Co${}_3$Sn${}_2$S${}_2$
• Magnetic Field Induced Quantum Metric Dipole in Dirac Semimetal Cd3As2
• Programmable, Spontaneous Superlattice Memory in a Monolayer Topological Insulator
• Parabolic Hall Effect due to Co-Propagating Surface Modes
• Anomalous Circularly Polarized Light Emission induced by the Optical Berry Curvature Dipole
• Precise determination of critical points of topological phase transitions via shift current in two-dimensional inversion asymmetric insulators
• Emergent Topological Semimetal
• Many-Body Quantum Geometric Dipole
• Quantum Nonlinear Acoustic Hall Effect and Inverse Acoustic Faraday Effect in Dirac Insulators
• The Future of the Correlated Electron Problem
• Topological Enhancement of Nonlinear Transports in Unconventional Point-Node Semimetals
• Facilitating field-free perpendicular magnetization switching with a Berry curvature dipole in a Weyl semimetal
• Theory of Nonlocal Transport from Nonlinear Valley Responses
• Nonlinear Transport Signatures of Hidden Symmetry Breaking in a Weyl Altermagnet
• Symmetry-driven Intrinsic Nonlinear Pure Spin Hall Effect
• Chirality-tunable non-linear Hall effect
• Hall effect evidence for an interplay between electronic correlations and Na order induced electronic bands topology in NaxCoO2
• Nonlinear longitudinal current of band-geometric origin in wires of finite thickness
• Odd-Parity Magnetism in Fe-Based Superconductors
• Quantum Metric-induced Oscillations in Flat Bands
• Approximate half-integer quantization in anomalous planar transport in $d$-wave altermagnets
• Trigonal warping effects on optical properties of anomalous Hall materials
• Tunable optical bistability of two-dimensional tilted Dirac system
• Vector Optical Activity in the Weyl Semimetal TaAs
• Topological Kondo semimetals emulated in hetero-bilayer transition metal dichalcogenides
• Nonlinear planar magnetotransport as a probe of the topology of surface states
• Role of Disorder in Third-order Anomalous Hall Effect in Time-reversal Symmetric Systems
• Orbital anomalous Hall effect in the few-layer Weyl semimetal TaIrTe4
• Two-Terminal Electrical Detection of the Néel Vector via Longitudinal Antiferromagnetic Nonreciprocal Transport
• The "Sign problem" of the 3rd order anomalous Hall effect in topological magnetic materials
• Nonlinear Hall response in the driving dynamics of ultracold atoms in optical lattices
• Magnus spin Hall and spin Nernst effects in gapped 2D Rashba systems
• Light-induced Nonlinear Spin Hall Current in Single-layer WTe${}_2$
• Quantized crystalline-electromagnetic responses in insulators
• Terahertz Spin-Light Coupling in Proximitized Dirac Materials
• Uniform and Staggered electric axial moment in zigzag chain
• Quantum theory of the magnetochiral anisotropy coefficient in ZrTe${}_5$
• Circular Photon Drag Effect in Dirac electrons by Quantum Geometry
• The Anomalous Hall Effect
• Universal intrinsic orbital dynamics from Berry curvature in electronic two-band systems
• Reexamining Circular Dichroism in Photoemission From a Topological Insulator
• Nodal-line semimetals and their variance
• Charge transport in chiral solids as a possible tool in search of dark matter signals
• Winding Berry dipole on uniaxially strained graphene/hBN/hBN moiré trilayers
• Signatures of valley drift in the diversified band dispersions of bright, gray, and dark excitons in MoS2 monolayers under uni-axial strains
• Projectively implemented altermagnetism in an exactly solvable quantum spin liquid
• Intra-cell dynamics and cyclotron motion without magnetic field
• Microscopic Theory of Nonlinear Hall Effect in Three-dimensional Magnetic Systems
• Giant Nonlinear Hall Effect in Twisted Bilayer WTe2
• Reconstructing the wavefunction of magnetic topological insulators MnBi2Te4 and MnBi4Te7 using spin-resolved photoemission
• Drude weights in one-dimensional systems with a single defect
• Probing Hidden Symmetry and Altermagnetism with Sub-Picometer Sensitivity via Nonlinear Transport
• Quantum Geometric Origin of Orbital Magnetization
• Linear magneto-conductivity as a DC probe of time-reversal symmetry breaking
• Surface spin polarization in the magnetic response of GeTe Rashba ferroelectric
• Large quantum nonreciprocity in plasmons dragged by drifting electrons
• Nonlinear response of 2DEG in the quantum Hall regime
• Nonlinear Hall effect driven by spin-charge-coupled motive force
• Berry curvature associated to Fermi arcs in continuum and lattice Weyl systems
• Odd-parity quadrupole order and induced nonreciprocal transport in the kagome metal CsTi${}_3$Bi${}_5$ driven by quantum interference
• Giant Room-Temperature Third-Order Electrical Transport in a Thin-Film Altermagnet Candidate
• Quadrupolar photovoltaic effect in the terahertz range in a two-dimensional spin-3/2 hole system
• Topological nature of in-gap bound states in disordered large-gap monolayer transition metal dichalcogenides
• Nonreciprocal Nonlinear Responses in Moving Charge Density Waves
• Wannier interpolation of spin accumulation coefficient
• Spin-valve effect for spin-polarized surface states in topological semimetals
• Unidirectional magneto-transport of linearly dispersing topological edge states
• Large circular photogalvanic effect in the noncentrosymmetric magnetic Weyl semimetal CeAlSi
• Topological Aspects of Antiferromagnets
• Singular nonlinear response in metals due to divergent Berry curvature: application to magneto-resistance in metals with type-II Weyl nodes
• Quantum metric non-linear Hall effect in an antiferromagnetic topological insulator thin-film EuSn2As2
• Spin Currents in Rashba Altermagnets: From Equilibrium to Nonlinear Regimes
• Quantum nonlinear ac transport theory at low frequency
• Second-Order Conductivity Probes a Cascade of Singularities in a Moiré Superlattice
• Nonlinear edge transport in a quantum Hall system
• Energy magnetization and transport in systems with a non-zero Berry curvature in a magnetic field
• Spin motive force by the momentum-space Berry phase in magnetic Weyl semimetals
• Probing domain wall dynamics in magnetic Weyl semimetals via the non-linear anomalous Hall effect
• 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
• Nonlinear Hall Effects induced by Berry Curvature Dipole in CuPb${}_9$(PO${}_4$)${}_6$O
• Hydrodynamic non-linear response of interacting integrable systems
• Nonlinear orbital response across topological phase transition in centrosymmetric materials
• Coulomb drag by motion of a monolayer polar crystal through graphene nanoconstriction
• Strong Field Optical Hall Effect in 2D Weyl Semimetal
• Large positive magnetoconductance in carbon nanoscrolls
• Nonlinear frequency-asymmetric optical response in chiral systems
• Resonant second harmonic generation in a two-dimensional electron system
• Problem of nonlinear conductivity within relaxation time approximation in noncentrosymmetric insulators
• Tunable linear and nonlinear anomalous Hall transport in two-dimensional CrPS${}_4$
• Spin-polarized scanning tunneling microscopy measurement scheme for determining the quantum geometric tensor
• Hallmarks of spin textures for high-harmonic generation in two-dimensional materials
• Orbital magnetization as the origin of the nonlinear Hall effect
• Temporal modulation of second harmonic generation in ferroelectrics by a pulsed electric field
• Berry Curvature Dipole-Induced Chiral Terahertz Gain and Lasing Threshold in Bulk Tellurium
• Diamagnetic Meissner response of odd-frequency superconducting pairing from quantum geometry
• Intrinsic nonlinear Hall effect beyond Bloch geometry
• Gradient flow and Bogomolny bounds for quantum metric actions
• Visible and Terahertz Nonlinear Responses in the Topological Noble Metal Dichalcogenide PdTe2
• Quantized nonlinear transport and its breakdown in Fermi gases with Berry curvature
• Quantum geometry in correlated electron phases: from flat band to dispersive band
• Nonlinear spin-Seebeck diode in $f$-wave magnets, third-order spin-Nernst effects in $g$-wave magnets and spin-Nernst effects in $i$-wave altermagnets
• Probing quantum geometric nonlinear magnetization via second-harmonic magneto-optical Kerr effect
• General method for calculating transport properties of disordered mesoscopic systems based on the nonequilibrium Green's function formalism
• Classification of spin Hall effect in two-dimensional systems
• Sign reversal of magnetoresistivity in massive nodal-line semimetals due to Lifshitz transition of Fermi surface
• Nonlinear response induced by Ferromagnetism in a Noncentrosymmetric Kondo Lattice system
• Evidence of Spin-Valley Coupling in Dirac Material BaMnBi2 Probed by Quantum Hall Effect and Nonlinear Hall Effect
• Optical Response from Charge-Density Waves in Weyl Semimetals
• Surface acoustic wave-driven valley current generation in intervalley coherent states
• Linear thermal noise induced by Berry curvature dipole in a four-terminal system
• Excitonic instability in transition metal dichalcogenides
• Tangent equations of motion for nonlinear response functions
• Numerical calculation of the $k$-space second Chern number in four dimensions
• Straintronics and twistronics in bilayer graphene
• Weak localization and antilocalization corrections to nonlinear transport: a semiclassical Boltzmann treatment
• Second-Order Synaptic Memory using Inherent Plasticity of Moiré Superlattices
• Ferroelectric-tunable quantum nonlinearity of chiral Bloch electrons in a moiré system
• Optical vortex probe of loop-current chirality in moiré materials
• Quantum geometric map of magnetotransport
• Hall Shift Current and Nonlinear Anomalous Hall Effect in Gapped Dirac Fermion Systems
• Third-order nonlinear transport in a percolative two-dimensional superconductor
• Prediction of a layer nonlinear Hall effect in bilayer nonmagnetic or antiferromagnetic systems
• Local phase-space Berry curvature and Hall transport in textured twisted bilayer graphene
• Electrotoroidicity: New Paradigm for Transverse Electromagnetic Responses
• Transverse Photoresistivity from Photothermal Current Deflection in Metal Films
• Design Principles for Topological Thermoelectrics
• Anomalous Transport Induced by Non-Hermitian Anomalous Berry Connection in Non-Hermitian Systems
• Quantum Christoffel Nonlinear Magnetization
• Intrinsic nonlinear valley Nernst effect
• Identification of chirality of chiral multifold fermions in anti-crystals
• Nonlinear Magnetoelectric Edelstein Effect
• Exploring Many-Body Quantum Geometry Beyond the Quantum Metric with Correlation Functions: A Time-Dependent Perspective
• Quantum theory of nonlinear electromagnetic response
• Intrinsic nonlinear valley Nernst effect in the strained bilayer graphene
• Imaginary Time Formalism for Causal Nonlinear Response Functions
• Unified theory of the photovoltaic Hall effect by field- and light-induced Berry curvatures
• Wavefunction-Free Approach for Predicting Nonlinear Responses in Weyl Semimetals
• Ratchet Hall Effect in Fluctuating Superconductors
• Probing the Quantum Geometry of Correlated Metals using Optical Conductivity
• Spontaneous Symmetry Breaking of Cavity Vacuum and Emergent Gyrotropic Effects in Embedded moiré Superlattices
• Long-time divergences in the nonlinear response of gapped one-dimensional many-particle systems
• Superconducting Berry Curvature Dipole
• Terahertz electro-optic effect in Bi${}_2$Se${}_3$ crystals
• General solution for the response of materials under radiation and tilted magnetic field: semi-classical regime
• Orbital optical activity in noncentrosymmetric metals and superconductors
• Electrons flow like falling cats: Deformations and emergent gravity in quantum transport
• Vortical currents and reciprocal relations for transport coefficients in the electron hydrodynamic regime
• Revealing the non-adiabatic and non-Abelian multiple-band effects via anisotropic valley Hall conduction in bilayer graphene
• Direct observation of the layer-number-dependent electronic structure in few-layer WTe2
• Nonlinear response functions and disorder: the case of photogalvanic effect
• Emerging nonlinear Hall effect in Kane-Mele two-dimensional topological insulators
• Calculation of Berry curvature using nonorthogonal atomic orbitals
• Magnetotransport in Topological Materials and Nonlinear Hall Effect via First-Principles Electronic Interactions and Band Topology
• Electric field controlled second-order anomalous Hall effect in altermagnets
• Identifying geometric third-order nonlinear transport in disordered materials
• Quantum geometric magnetic monopole and two-phase superconductivity in CeRh${}_2$As${}_2$
• Geometric Effects on Tunneling in Driven Quantum Systems
• Resonant Nonlinear Hall Effect in Two-Dimensional Electron Systems
• Dissipation-Shaped Quantum Geometry in Nonlinear Transport
• Nonlinear Odd Viscoelastic Effect
• Theory of unidirectional magnetoresistance and nonlinear Hall effect
• Nonlinear Hall effect as a local probe of plasmonic magnetic hot spots