Equivalence of semiclassical and response theories for second-order nonlinear ac Hall effects

Abstract

It has been known that the semiclassical theory and the response theory can equivalently give the Drude and the intrinsic anomalous Hall conductivities in the linear order of electric field. However, recent theoretical advances implied that the second-order nonlinear conductivities calculated with both approaches are no longer equivalent, which leads to various experimental explanations even in a similar experimental setup conducted in \href{https://www.science.org/doi/10.1126/science.adf1506}{[\textit{Science \textbf{381}, 181 (2023)}]} and \href{https://www.nature.com/articles/s41586-023-06363-3}{[\textit{Nature \textbf{621}, 487 (2023)}]}, respectively. Herein, by extending the AC semiclassical theory up to the second order of electric field, we show that the semiclassical theory is still equivalent to the response theory in the second order of electric field when the relaxation is taken into account on the same footing. In particular, we show that the familiar second-order nonlinear current responses, including the nonlinear Drude current and the Berry curvature (quantum metric) dipole driven extrinsic (intrinsic) nonlinear Hall current, can be derived by both approaches. Further, we show that the quantum-corrected intrinsic nonlinear longitudinal current, as recently proposed by the response theory or in a similar manner, can also be reproduced by the semiclassical theory. Beyond those known second-order current responses, with both approaches, we uncover two previously overlooked nonlinear displacement currents unique to the AC electric field. As a consequence of this equivalence,...

published in Physical Review B

References in corpus (29)

• First Principles Calculation of Anomalous Hall Conductivity in Ferromagnetic bcc Fe
• 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
• Essay: Where Can Quantum Geometry Lead Us?
• Unification of Nonlinear Anomalous Hall Effect and Nonreciprocal Magnetoresistance in Metals by the Quantum Geometry
• Photocurrent as a multi-physics diagnostic of quantum materials
• Quantum geometry induced second harmonic generation
• Emergent Electromagnetic Induction and Adiabatic Charge Pumping in Weyl Semimetals
• Quantum Kinetic Theory of the Chiral Anomaly
• Intrinsic Nonlinear Spin Magnetoelectricity in Centrosymmetric Magnets
• Orbital Magneto-Nonlinear Anomalous Hall Effect in Kagome Magnet Fe${}_3$Sn${}_2$
• Tunable moiré materials for probing Berry physics and topology
• Orbital Origin of Intrinsic Planar Hall Effect
• Anomalous skew-scattering nonlinear Hall effect and chiral photocurrents in {\it PT}-symmetric antiferromagnets
• Unifying semiclassics and quantum perturbation theory at nonlinear order
• Dominance of extrinsic scattering mechanisms in the orbital Hall effect: graphene, transition metal dichalcogenides and topological antiferromagnets
• Time-Reversal Even Charge Hall Effect from Twisted Interface Coupling
• Engineering transistor-like optical gain in two-dimensional materials with Berry curvature dipoles
• Third-order intrinsic anomalous Hall effect with generalized semiclassical theory
• General nonlinear Hall current in magnetic insulators beyond the quantum anomalous Hall effect
• Quantum geometry quadrupole-induced third-order nonlinear transport in antiferromagnetic topological insulator MnBi2Te4
• Third-order Hall effect in the surface states of a topological insulator
• Quantum kinetic theory of nonlinear thermal current
• High-efficiency energy harvesting based on nonlinear Hall rectifier
• Disorder in the non-linear anomalous Hall effect of $\mathcal{P}\mathcal{T}$-symmetric Dirac fermions
• Ab initio study of the nonlinear optical properties and d.c. photocurrent of the Weyl semimetal TaIrTe${}_4$
• Berry Curvature Spectroscopy from Bloch Oscillations

Cited by in corpus (15)

• 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
• Intrinsic gyrotropic magnetic current from Zeeman quantum geometry
• A Clarification on Quantum-Metric-Induced Nonlinear Transport
• Non-linear anomalous Edelstein response at altermagnetic interfaces
• Proper Definition of Intrinsic Nonlinear Current
• Quantum Geometric Origin of the Intrinsic Nonlinear Hall Effect
• Two-Terminal Electrical Detection of the Néel Vector via Longitudinal Antiferromagnetic Nonreciprocal Transport
• Quantum kinetic theory of the semiclassical side jump, skew scattering and longitudinal velocity
• Quantum Christoffel Nonlinear Magnetization
• Intraband circular photogalvanic effect in Weyl semimetals
• Nonlinear Magnetoelectric Edelstein Effect
• Quantum geometric map of magnetotransport
• Identifying geometric third-order nonlinear transport in disordered materials