Quantum kinetic theory of quadratic responses
arXiv:2409.14539 · doi:10.1103/PhysRevB.110.174423
Abstract
Recent work has revealed a general procedure for incorporating disorder into the semiclassical model of carrier transport, whereby the predictions of quantum linear response theory can be recovered within a quantum kinetic approach based on a disorder-averaged density-matrix formalism. Here, we present a comprehensive generalization of this framework to the nonlinear response regime. In the presence of an electrostatic potential and random impurities, we solve the quantum Liouville equation to second order in an applied electric field and derive the carrier densities and equations of motion. In addition to the anomalous velocity arising from the Berry curvature and the Levi-Civita connection of the quantum metric tensor, a host of extrinsic velocities emerge in the equations of motion, reflecting the various possibilities for random interband walks of the carriers in this transport regime. Furthermore, several scattering and conduction channels arise, which can be classified in terms of distinct physical processes, revealing numerous unexplored mechanisms for generating nonlinear responses in disordered condensed matter systems.
30 pages, 2 figures. To be published in Physical Review B
References in corpus (92)
- Berry Phase Effects on Electronic Properties
- Anomalous Hall effect
- Quantum nonlinear Hall effect induced by Berry curvature dipole in time-reversal invariant materials
- Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects
- Anomalous Hall effect arising from noncollinear antiferromagnetism
- Observation of the nonlinear Hall effect under time reversal symmetric conditions
- Berry phase, hyperorbits, and the Hofstadter spectrum: semiclassical dynamics in magnetic Bloch bands
- Ab initio calculation of the anomalous Hall conductivity by Wannier interpolation
- Unidirectional spin Hall magnetoresistance in ferromagnet/normal metal bilayers
- Field Induced Positional Shift of Bloch Electrons and its Dynamical Implications
- Tilted anisotropic Dirac cones in quinoid-type graphene and alpha-(BEDT-TTF)_2I_3
- Nonlinear Hall Effects
- Semiclassical theories of the anomalous Hall effect
- Quantum metric nonlinear Hall effect in a topological antiferromagnetic heterostructure
- Anomalous Hall effect in 2D Dirac band: link between Kubo-Streda formula and semiclassical Boltzmann equation approach
- Quantum metric-induced nonlinear transport in a topological antiferromagnet
- Berry phase, hyperorbits, and the Hofstadter spectrum
- Disorder-induced nonlinear Hall effect with time-reversal symmetry
- Intrinsic nonlinear Hall effect in antiferromagnetic tetragonal CuMnAs
- 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
- Intrinsic Second-Order Anomalous Hall Effect and Its Application in Compensated Antiferromagnets
- Large Unidirectional Magnetoresistance in a Magnetic Topological Insulator
- Berry curvature dipole current in transition metal dichalcogenides family
- Bilinear magneto-electric resistance as a probe of three-dimensional spin texture in topological surface states
- Fermi-surface calculation of the anomalous Hall conductivity
- Current-nonlinear Hall effect and spin-orbit torque magnetization switching in a magnetic topological insulator
- Strongly enhanced Berry dipole at topological phase transitions in BiTeI
- Quantum theory of the nonlinear Hall effect
- 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
- Nonlinear planar Hall effect
- Giant Orbital Magneto-electric effect and Current-driven Magnetization Switching in Twisted Bilayer Graphene
- Berry curvature unravelled by the Nernst effect in MnGe
- Weyl fermions and the anomalous Hall effect in metallic ferromagnets
- Origins of the unidirectional spin Hall magnetoresistance in metallic bilayers
- Coordinate shift in the semiclassical Boltzmann equation and the anomalous Hall effect
- Theory of nonlinear Hall effects: renewed semiclassics from quantum kinetics
- Negative Magnetoresistance without Chiral Anomaly in Topological Insulators
- Nonlinear Hall effect with time-reversal symmetry: Theory and material realizations
- Topological currents in black phosphorus with broken inversion symmetry
- Quantum geometry induced second harmonic generation
- Disorder effects in the AHE induced by Berry curvature
- Theory of unidirectional spin Hall magnetoresistance in heavy-metal/ferromagnetic-metal bilayers
- Inter-band Coherence Response to Electric Fields in Crystals
- Electrical detection of magnetization reversal without auxiliary magnets
- Magnetoresistance of heavy and light metal/ferromagnet bilayers
- Observation of Large Unidirectional Rashba Magnetoresistance in Ge(111)
- Nonlinear transport in Weyl semimetals induced by Berry curvature dipole
- Quantum geometry in condensed matter
- Quantum Kinetic Theory of the Chiral Anomaly
- Generating a topological anomalous Hall effect in a non-magnetic conductor
- Fluctuations, uncertainty relations, and the geometry of quantum state manifolds
- Theory of bi-linear magnetoresistance within the minimal model for surface states in topological insulators
- Nonlinear Hall effect in Weyl semimetals induced by chiral anomaly
- Berry phase and Anomalous Hall Effect in a Three-orbital Tight-binding Hamiltonian
- Resonant photovoltaic effect in doped magnetic semiconductors
- Anomalous skew-scattering nonlinear Hall effect and chiral photocurrents in {\it PT}-symmetric antiferromagnets
- Chirality induced Giant Unidirectional Magnetoresistance in Twisted Bilayer Graphene
- Semiclassical equations of motion for disordered conductors: extrinsic interband velocity, corrected collision integral and spin-orbit torques
- Giant unidirectional magnetoresistance in topological insulator -- ferromagnetic semiconductor heterostructures
- Unifying semiclassics and quantum perturbation theory at nonlinear order
- Berry Curvature Engineering by Gating Two-Dimensional Antiferromagnets
- Unidirectional orbital magnetoresistance in light metal/ferromagnet bilayers
- Valley Hall effect in disordered monolayer MoS2 from first principles
- General nonlinear Hall current in magnetic insulators beyond the quantum anomalous Hall effect
- Semiclassical theory of spin-orbit torques in disordered multiband electron systems
- Gauge invariance and Ward identities in nonlinear response theory
- Unidirectional Magnetoresistance in Antiferromagnet/Heavy-metal bilayers
- Quantum Kinetic Theory of Nonlinear Optical Currents: Finite Fermi surface and Fermi sea contributions
- How disorder affects the Berry-phase anomalous Hall conductivity: the view from k space
- Quantum kinetic theory of nonlinear thermal current
- Unidirectional Spin Hall Magnetoresistance in Antiferromagnetic Heterostructures
- Disorder in the non-linear anomalous Hall effect of -symmetric Dirac fermions
- Large anomalous unidirectional magnetoresistance in a single ferromagnetic layer
- Large Rashba unidirectional magnetoresistance in the Fe/Ge(111) interface states
- Observation of nonlinear planar Hall effect in magnetic insulator/topological insulator heterostructures
- Temperature dependence of side-jump spin Hall conductivity
- Superconducting Orbital Magnetoelectric Effect and its Evolution across the Superconductivity Normal Metal Phase Transition
- Large Bilinear Magnetoresistance from Rashba Spin-Splitting on the Surface of a Topological Insulator
- Large Unidirectional Magnetoresistance in Metallic Heterostructures in the Spin Transfer Torque Regime
- Tunable valley Hall effect in gate-defined graphene superlattices
- Bilinear magnetoresistance in HgTe topological insulator: opposite signs at opposite interfaces demonstrated by gate control
- Spin anomalous-Hall unidirectional magnetoresistance
- Charge Conservation Beyond Uniformity: Spatially Inhomogeneous Electromagnetic Response in Periodic Solids
- Electrical Magnetochiral current in Tellurium
- Intrinsic nonlinear Hall effect in two-dimensional honeycomb topological antiferromagnets
- Nonreciprocal Ballistic Transport in Asymmetric Bands
- Quantum unidirectional magnetoresistance
- Proximity-induced nonlinear magnetoresistances on topological insulators
- Nonlinear magnetotransport in MoTe
Cited by in corpus (13)
- Quantum geometry in condensed matter
- Revealing Quantum Geometry in Nonlinear Quantum Materials
- Non-linear Transport in Non-centrosymmetric Systems: From Fundamentals to Applications
- Scaling Law for Time-Reversal-Odd Nonlinear Transport
- Surface-Dominated Quantum Metric-Induced Nonlinear Transport in the Layered Antiferromagnet CrSBr
- Quantum response theory and momentum-space gravity
- Interband contributions to nonlinear transport in semiconductor nanostructures
- Quantum Geometric Origin of the Intrinsic Nonlinear Hall Effect
- Quantum metric non-linear Hall effect in an antiferromagnetic topological insulator thin-film EuSn2As2
- Quantum kinetic theory of the semiclassical side jump, skew scattering and longitudinal velocity
- Comparing the Extrinsic Orbital Hall Effect in Centrosymmetric and Noncentrosymmetric Systems: Insights from Bilayer Transition Metal Dichalcogenides
- Nonlinear Odd Viscoelastic Effect
- Dissipation-Shaped Quantum Geometry in Nonlinear Transport