Quantum kinetic equation in phase-space textured multiband systems

Abstract

Starting from the density-matrix equation of motion, we derive a semiclassical kinetic equation for a general two-band electronic Hamiltonian, systematically including quantum-mechanical corrections up to second order in space-time gradients. We find, in addition to band-projected corrections to the single-particle equation of motion due to phase-space Berry curvature, interband terms that we attribute to the nonorthorgonality of the projected Hilbert spaces. As examples, we apply our kinetic equation to electronic systems in the presence of spatially inhomogeneous and dynamical spin textures stemming from electromagnetic gauge potentials. Specifically, we consider the electromagnetic response of massive two-dimensional Dirac fermions and three-dimensional Weyl fermions, and reproduce the anomalous currents known as the parity and the Adler-Bell-Jackiw anomaly in particle physics.

References in corpus (7)

• Topological Insulators
• Berry phase effect in anomalous thermoelectric transport
• Berry phase mediated topological thermoelectric transport in gapped single and bilayer graphene
• Semiclassical dynamics and transport of the Dirac spin
• Gradient expansion approach to multiple-band Fermi liquids
• Artificial electric field in Fermi Liquids
• Geometrical phase effects on the Wigner distribution of Bloch electrons

Cited by in corpus (21)

• Berry Curvature, Triangle Anomalies, and the Chiral Magnetic Effect in Fermi Liquids
• Chiral Kinetic Theory
• Kinetic theory with Berry curvature from quantum field theories
• Berry curvature and 4-dimensional monopole in relativistic chiral kinetic equation
• Chiral magnetic effect and natural optical activity in (Weyl) metals
• Kinetic theory of chiral relativistic plasmas and energy density of their gauge collective excitations
• Large enhancement of conductivity in Weyl semimetals with tilted cones: Pseudorelativity and linear response
• Quantum kinetic theory for spin-1/2 fermions in Wigner function formalism
• Dirac sea and chiral anomaly in the quantum kinetic theory
• Photo-Induced Anomalous Hall Effect in Two-Dimensional Transition-Metal Dichalcogenides
• Kinetic orbital moments and nonlocal transport in disordered metals with nontrivial geometry
• Quantum kinetics of anomalous and nonlinear Hall effects in topological semimetals
• Effective Quantum Theories for Transport in Inhomogeneous Systems with Non-trivial Band Structure
• Quasiparticle Berry curvature and Chern numbers in spin-orbit coupled bosonic Mott insulators
• Derivation of Semiclassical Kinetic Theory in the Presence of Non-Abelian Berry Curvature
• Quantum Transport Theory of Strongly Correlated Matter
• Weyl systems: anomalous transport normally explained
• Covariant Chiral Kinetic Equation in Non-Abelian Gauge field from "covariant gradient expansion"
• Phase space curvature in spin-orbit coupled ultracold atom systems
• Topological fluctuating electron-hole Cooper pairs in graphene-GaAs heterostructures
• Gradient expansion of the non-Abelian gauge-covariant Moyal star-product