Intrinsic anomalous Hall conductivity in a nonuniform electric field
arXiv:2010.07322 · doi:10.1103/PhysRevLett.126.156602
Abstract
We study how the intrinsic anomalous Hall conductivity is modified in two-dimensional crystals with broken time-reversal symmetry due to weak inhomogeneity of the applied electric field. Focusing on a clean noninteracting two-band system without band crossings, we derive the general expression for the Hall conductivity at small finite wave vector to order , which governs the Hall response to the second gradient of the electric field. Using the Kubo formula, we show that the answer can be expressed through the Berry curvature, Fubini-Study quantum metric, and the rank-3 symmetric tensor which is related to the quantum geometric connection and physically corresponds to the gauge-invariant part of the third cumulant of the position operator. We further compare our results with the predictions made within the semiclassical approach. By deriving the semiclassical equations of motion, we reproduce the result obtained from the Kubo formula in some limits. We also find, however, that the conventional semiclassical description in terms of the definite position and momentum of the electron is not fully consistent because of singular terms originating from the Heisenberg uncertainty principle. We thus present a clear example of a case when the semiclassical approach inherently suffers from the uncertainty principle, implying that it should be applied to systems in nonuniform fields with extra care.
References in corpus (28)
- Topological Insulators
- Topological insulators and superconductors
- Berry Phase Effects on Electronic Properties
- Maximally-localized generalized Wannier functions for composite energy bands
- Anomalous Hall effect
- Weyl and Dirac Semimetals in Three Dimensional Solids
- Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects
- Berry Curvature on the Fermi Surface: Anomalous Hall Effect as a Topological Fermi-Liquid Property
- Berry phase, hyperorbits, and the Hofstadter spectrum: semiclassical dynamics in magnetic Bloch bands
- Field Induced Positional Shift of Bloch Electrons and its Dynamical Implications
- Polarization and localization in insulators: generating function approach
- Hall Viscosity and Electromagnetic Response
- Measuring Hall Viscosity of Graphene's Electron Fluid
- Kubo formulas for viscosity: Hall viscosity, Ward identities, and the relation with conductivity
- Low-frequency divergence and quantum geometry of the bulk photovoltaic effect in topological semimetals
- Gyrotropic magnetic effect and the magnetic moment on the Fermi surface
- Hydrodynamic Electron Flow and Hall Viscosity
- Electron localization in the insulating state: application to crystalline semiconductors
- Chiral magnetic effect and natural optical activity in (Weyl) metals
- Resonance-enhanced optical nonlinearity in the Weyl semimetal TaAs
- Nonreciprocal Directional Dichroism Induced by the Quantum Metric Dipole
- Transport signatures of Hall viscosity
- Semi-classical wave packet dynamics in non-uniform electric fields
- Unified description of the classical Hall viscosity
- Hall viscosity in quantum systems with discrete symmetry: point group and lattice anisotropy
- Nonadiabatic wavepacket dynamics: k-space formulation
- Finite-wavevector Electromagnetic Response in Lattice Quantum Hall Systems
- Geometric response of quantum Hall states to electric fields
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- Riemannian geometry of resonant optical responses
- The Ginzburg-Landau theory of flat band superconductors with quantum metric
- Nontrivial Quantum Geometry and the Strength of Electron-Phonon Coupling
- Semiclassical equations of motion for disordered conductors: extrinsic interband velocity, corrected collision integral and spin-orbit torques
- Nontrivial quantum geometry of degenerate flat bands
- Origin of band flatness and constraints of higher Chern numbers
- Beyond the Berry Phase: Extrinsic Geometry of Quantum States
- Geometric Stiffness in Interlayer Exciton Condensates
- Instantaneous response and quantum geometry of insulators
- Interplay of Band Geometry and Topology in Ideal Chern Insulators in Presence of External Electromagnetic Fields
- The multi-state geometry of shift current and polarization
- Quantum entanglement and quantum geometry measured with inelastic X-ray scattering
- Drude weight and the many-body quantum metric in one-dimensional Bose systems
- Cubic Hall viscosity in three-dimensional topological semimetals
- Black hole mirages: electron lensing and Berry curvature effects in inhomogeneously tilted Weyl semimetals
- Geometric Origin of Intrinsic Spin Hall Effect in an Inhomogeneous Electric Field
- Charge Conservation Beyond Uniformity: Spatially Inhomogeneous Electromagnetic Response in Periodic Solids
- Mapping the intrinsic photocurrent streamlines through micromagnetic heterostructure devices
- Quantum Geometry and the Hidden Scales in Materials
- Supersymmetry on the lattice: Geometry, Topology, and Flat Bands
- Gravitational Response of Topological Quantum States of Matter
- Low-energy optical absorption in correlated insulators: Projected sum rules and the role of quantum geometry
- Current-induced quasiparticle magnetic multipole moments
- Quantum geometric tensor and the topological characterization of the extended Su-Schrieffer-Heeger model
- Noncommutative Geometry and Deformation Quantization in the Quantum Hall Fluids with Inhomogeneous Magnetic Fields
- Geometric semimetals and their simulation in synthetic matter
- Universal intrinsic orbital dynamics from Berry curvature in electronic two-band systems
- Quantum theory of nonlinear electromagnetic response
- Electrons flow like falling cats: Deformations and emergent gravity in quantum transport