Quantum kinetics of anomalous and nonlinear Hall effects in topological semimetals

Abstract

We present a systematic microscopic derivation of the semiclassical Boltzmann equation for band structures with the finite Berry curvature based on Keldysh technique of nonequilibrium systems. In the analysis, an ac electrical driving field is kept up to quadratic order, and both cases of small and large frequencies corresponding to intra- and interband transitions are considered. In particular, this formulation is suitable for the study of nonlinear Hall effect and photogalvanic phenomena. The role of impurity scattering is carefully addressed. Specifically, in addition to previously studied side-jump and skew-scattering processes, quantum interference diffractive contributions are now explicitly incorporated within the developed framework. This theory is applied to multifold fermions in topological semimetals, for which the generic formula for the skew scattering rate from the Pancharatnam phase is obtained along with the corresponding anomalous Hall conductivity.

Contribution to the Philip W. Anderson Memorial Special Issue in Annals of Physics [24 pages, 5 figures]

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Cited by in corpus (13)

• Nonlinear Hall Effects
• Intrinsic nonlinear Hall effect in antiferromagnetic tetragonal CuMnAs
• Revealing Quantum Geometry in Nonlinear Quantum Materials
• Semiclassical equations of motion for disordered conductors: extrinsic interband velocity, corrected collision integral and spin-orbit torques
• Valley and spin accumulation in ballistic and hydrodynamic channels
• Hall Coulomb drag induced by electron-electron skew scattering
• Quantum kinetic theory of the semiclassical side jump, skew scattering and longitudinal velocity
• Extrinsic contribution to bosonic thermal Hall transport
• The spin Hall effect
• Hydrodynamic Coulomb drag in odd electron liquids
• Resonant second harmonic generation in a two-dimensional electron system
• Stokes flow in an electronic fluid with odd viscosity
• Identifying geometric third-order nonlinear transport in disordered materials