Unification of Nonlinear Anomalous Hall Effect and Nonreciprocal Magnetoresistance in Metals by the Quantum Geometry

Abstract

The quantum geometry has significant consequences in determining transport and optical properties in quantum materials. Here, we use a semiclassical formalism coupled with perturbative corrections unifying the nonlinear anomalous Hall effect (NLAHE) and nonreciprocal magnetoresistance (NMR, longitudinal resistance) from the quantum geometry. In the dc limit, both transverse and longitudinal nonlinear conductivities include a term due to the normalized quantum metric dipole. The quantum metric contribution is intrinsic and does not scale with the quasiparticle lifetime. We demonstrate the coexistence of a NLAHE and NMR in films of the doped antiferromagentic topological insulator MnBi${}_2$Te${}_4$. Our work indicates that both longitudinal and transverse nonlinear transport provide a sensitive probe of the quantum geometry in solids.

4.5 pages; 2 figures. SI. Comments welcomed

References in corpus (25)

• Nonlinear Hall Effects
• Layer Hall effect in a 2D topological Axion antiferromagnet
• Quantum metric-induced nonlinear transport in a topological antiferromagnet
• Riemannian geometry of resonant optical responses
• Intrinsic nonlinear Hall effect in antiferromagnetic tetragonal CuMnAs
• Room temperature nonlinear Hall effect and wireless RF rectification in Weyl semimetal TaIrTe4
• The Berry curvature dipole in Weyl semimetal materials: an ab initio study
• Intrinsic Second-Order Anomalous Hall Effect and Its Application in Compensated Antiferromagnets
• Large Unidirectional Magnetoresistance in a Magnetic Topological Insulator
• Intertwined Topological and Magnetic Orders in Atomically Thin Chern Insulator MnBi2Te4
• Terahertz detection based on nonlinear Hall effect without magnetic field
• Giant $c$-axis nonlinear anomalous Hall effect in T${}_d$-MoTe${}_2$ and WTe${}_2$
• Nonlinear electric transport in odd-parity magnetic multipole systems: Application to Mn-based compounds
• Native Defects in Antiferromagnetic Topological Insulator MnBi${}_2$Te${}_4$
• Systematic analysis method for nonlinear response tensors
• 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
• Chirality induced Giant Unidirectional Magnetoresistance in Twisted Bilayer Graphene
• Unifying semiclassics and quantum perturbation theory at nonlinear order
• Distinct magnetic gaps between antiferromagnetic and ferromagnetic orders driven by surface defects in the topological magnet MnBi2Te4
• General nonlinear Hall current in magnetic insulators beyond the quantum anomalous Hall effect
• Extrinsic and Intrinsic Nonlinear Hall Effects across Berry-Dipole Transitions
• Momentum-inversion symmetry breaking on the Fermi surface of magnetic topological insulators
• Effects of relaxation on photovoltaic effect and possibility of photocurrent within transparent region
• Facet dependent surface energy gap on magnetic topological insulators

Cited by in corpus (90)

• Quantum geometry induced nonlinear transport in altermagnets
• Quantum geometry in condensed matter
• 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 Transport in Non-centrosymmetric Systems: From Fundamentals to Applications
• Quantum geometry quadrupole-induced third-order nonlinear transport in antiferromagnetic topological insulator MnBi2Te4
• The quantum metric of electrons with spin-momentum locking
• Odd-parity Magnetism Driven by Antiferromagnetic Exchange
• Magnetochiral Charge Pumping due to Charge Trapping and Skin Effect in Chirality-Induced Spin Selectivity
• Scaling Law for Time-Reversal-Odd Nonlinear Transport
• Magnetic geometry induced quantum geometry and nonlinear transports
• Anomalous Coherence Length in Superconductors with Quantum Metric
• An antiferromagnetic diode effect in even-layered MnBi2Te4
• Quantum Geometric Kohn-Luttinger Superconductivity
• Equivalence of semiclassical and response theories for second-order nonlinear ac Hall effects
• Light-enhanced nonlinear Hall effect
• Analytic approach to quantum metric and optical conductivity in Dirac models with parabolic mass in arbitrary dimensions
• Quasi-symmetry Constrained Spin Ferromagnetism in Altermagnets
• Intrinsic nonlinear conductivity induced by quantum geometry in altermagnets and measurement of the in-plane Néel vector
• Quantum Metric in Step Response
• General theory for longitudinal nonreciprocal charge transport
• Quantum Geometry Probed by Chiral Excitonic Optical Response of Chern Insulators
• Corner Charge Fluctuation as an Observable for Quantum Geometry and Entanglement in Two-dimensional Insulators
• Drude weight of an interacting flat-band metal
• Intrinsic gyrotropic magnetic current from Zeeman quantum geometry
• Quantum Geometry and the Hidden Scales in Materials
• Purely electrical detection of the spin-splitting vector in $p$-wave magnets based on linear and nonlinear conductivities
• Anomalous geometric transport signatures of topological Euler class
• Planar Hall Plateau in Magnetic Weyl Semimetals
• Hybrid-order topology in unconventional magnets of Eu-based Zintl compounds with surface-dependent quantum geometry
• Magnetic parity violation and parity-time-reversal-symmetric magnets
• Scaling of the Integrated Quantum Metric in Disordered Topological Phases
• Nonlinear electrical transport unveils Fermi surface malleability in a moiré heterostructure
• Quantum-metric-induced quantum Hall conductance inversion and reentrant transition in fractional Chern insulators
• Nonlinear Hall effect and scaling law in Sb-doped topological insulator MnBi4Te7
• Intrinsic nonlinear Hall effect in two-dimensional honeycomb topological antiferromagnets
• Symmetry Origin and Microscopic Mechanism of Electrical Magnetochiral Anisotropy in Tellurium
• TensorSymmetry: a package to get symmetry-adapted tensors disentangling spin-orbit coupling effect and establishing analytical relationship with magnetic order
• Second harmonic generation induced by gate voltage oscillation in few layer MnBi2Te4
• Anomalous Nonlinear Magnetoconductivity in van der Waals Magnet CrSBr
• Surface-Dominated Quantum Metric-Induced Nonlinear Transport in the Layered Antiferromagnet CrSBr
• Quantum geometry and elliptic optical dichroism in $p$-wave magnets
• Non-linear anomalous Edelstein response at altermagnetic interfaces
• Electrical control of intrinsic nonlinear Hall effect in antiferromagnetic topological insulator sandwiches
• Geometric and conventional contributions of superconducting diode effect: Application to flat-band systems
• A Clarification on Quantum-Metric-Induced Nonlinear Transport
• Phase shifts, band geometry and responses in triple-Q charge and spin density waves
• Nonreciprocal Ballistic Transport in Asymmetric Bands
• Quantum geometry and $X$-wave magnets with $X=p,d,f,g,i$
• Proper Definition of Intrinsic Nonlinear Current
• Geometrical Nonlinear Hall Effect Induced by Lorentz Force
• Nonlinear Hall effects with an exceptional ring
• Nonlinear and nonreciprocal transport effects in untwinned thin films of ferromagnetic Weyl metal SrRuO${}_3$
• Electrical magnetochiral anisotropy and quantum metric in chiral conductors
• Quantum geometry and the electric magnetochiral anisotropy in noncentrosymmetric polar media
• Quantum Geometric Origin of the Intrinsic Nonlinear Hall Effect
• Magnetic Field Induced Quantum Metric Dipole in Dirac Semimetal Cd3As2
• Nonlinear Transport Signatures of Hidden Symmetry Breaking in a Weyl Altermagnet
• Nonlinear planar magnetotransport as a probe of the topology of surface states
• Two-Terminal Electrical Detection of the Néel Vector via Longitudinal Antiferromagnetic Nonreciprocal Transport
• Symmetry-driven Intrinsic Nonlinear Pure Spin Hall Effect
• On the angular dependence of anomalous Hall current
• Role of Disorder in Third-order Anomalous Hall Effect in Time-reversal Symmetric Systems
• Quantum Metric-induced Oscillations in Flat Bands
• Quantum theory of the magnetochiral anisotropy coefficient in ZrTe${}_5$
• Nonlinear Hall effect driven by spin-charge-coupled motive force
• Circular Photon Drag Effect in Dirac electrons by Quantum Geometry
• Quantum geometric tensors from sub-bundle geometry
• Superfluid stiffness of superconductors with delicate topology
• Probing Hidden Symmetry and Altermagnetism with Sub-Picometer Sensitivity via Nonlinear Transport
• Giant Room-Temperature Third-Order Electrical Transport in a Thin-Film Altermagnet Candidate
• C-type antiferromagnetic structure of topological semimetal CaMnSb${}_2$
• Quantum Geometric Origin of Orbital Magnetization
• Room temperature quantum metric effect in TbMn6Sn6
• Geometric transport signatures of strained multi-Weyl semimetals
• Dynamics and transport of Bose-Einstein condensates in bent potentials
• Nonreciprocal ballistic transport in multi-layer Weyl semimetal films with surface engineering
• Quantum geometry, localization, and topological bounds of spin fluctuations
• Orbital magnetization as the origin of the nonlinear Hall effect
• 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
• Strain effect on optical properties and quantum weight of monolayer MnBi${}_2$X${}_4$ (X = Te, Se, S)
• Nonlinear Magnetoelectric Edelstein Effect
• Quantum geometric map of magnetotransport
• Intrinsic nonlinear valley Nernst effect in the strained bilayer graphene
• Prediction of a layer nonlinear Hall effect in bilayer nonmagnetic or antiferromagnetic systems
• Identifying geometric third-order nonlinear transport in disordered materials
• Electric field controlled second-order anomalous Hall effect in altermagnets
• Third-order nonlinear transport in a percolative two-dimensional superconductor
• Dissipation-Shaped Quantum Geometry in Nonlinear Transport
• Surface acoustic wave-driven valley current generation in intervalley coherent states