Wigner transformation, momentum space topology, and anomalous transport

Abstract

Using derivative expansion applied to the Wigner transform of the two - point Green function we analyse the anomalous quantum Hall effect (AQHE), and the chiral magnetic effect (CME). The corresponding currents are proportional to the momentum space topological invariants. We reproduce the conventional expression for the Hall conductivity in $2+1$ D. In $3+1$ D our analysis allows to explain systematically the AQHE in topological insulators and Weyl semimetals. At the same time using this method it may be proved, that the equilibrium CME is absent in the wide class of solids, as well as in the properly regularized relativistic quantum field theory.

Latex, 26 pages, misprints corrected

References in corpus (7)

• Topological response in Weyl semimetals and the chiral anomaly
• Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals
• Chiral Magnetic conductivity
• Four-dimensional graphene and chiral fermions
• Absence of Luttinger's Theorem due to Zeros in the Single-Particle Green Function
• Absence of equilibrium chiral magnetic effect
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Cited by in corpus (28)

• Elasticity tetrads, mixed axial-gravitational anomalies, and 3+1d quantum Hall effect
• Chiral torsional effect
• Chiral Separation Effect in lattice regularization
• Anatomy of the chiral vortical effect
• Hall conductivity as the topological invariant in phase space in the presence of interactions and non-uniform magnetic field
• Influence of interactions on the anomalous quantum Hall effect
• Scale Magnetic Effect in Quantum Electrodynamics and the Wigner-Weyl Formalism
• Standard Model as the topological material
• Topological invariant in terms of the Green functions for the Quantum Hall Effect in the presence of varying magnetic field
• Chiral Separation effect in non-homogeneous systems
• A Note on Bloch theorem
• Effect of interactions on the topological expression for the chiral separation effect
• The black hole interior and the type II Weyl fermions
• Hall effect in the presence of rotation
• Precise Wigner-Weyl calculus for lattice models
• Feynman Rules in terms of the Wigner transformed Green functions
• Momentum Space Topology and Non-Dissipative Currents
• Wigner-Weyl calculus in Keldysh technique
• Phase-space elementary information content of confined Dirac spinors
• TKNN formula for general Hamiltonian
• Anomalous transport phenomena and momentum space topology
• Hall conductivity as topological invariant in phase space
• Hall conductivity as the topological invariant in magnetic Brillouin zone in the presence of interactions
• Classification of emergent Weyl spinors in multi-fermion systems
• Discrete Wigner-Weyl calculus for the finite lattice
• Magneto-conductivity and CME in Dirac semimetals from Keldysh technique in Landau levels basis
• Topological invariant of multilayer Haldane models with irregular stackings
• Hall conductivity of strained $Z_2$ crystals