Disorder Induced Anomalous Hall Effect in Type-I Weyl Metals: Connection between the Kubo-Streda Formula in the Spin and Chiral basis

Abstract

We study the anomalous Hall effect (AHE) in tilted Weyl metals with weak Gaussian disorder under the Kubo-Streda formalism in this work. To separate the three different contributions, namely the intrinsic, side jump and skew scattering contribution, it is usually considered necessary to go to the eigenstate (chiral) basis of the Kubo-Streda formula. However, it is more straight-forward to compute the total Hall current in the spin basis. For the reason, we develop a systematic and transparent scheme to separate the three different contributions in the spin basis for relativistic systems by building a one-to-one correspondence between the Feynman diagrams of the different mechanisms in the chiral basis and the products of the symmetric and anti-symmetric part of the polarization operator in the spin basis. We obtain the three contributions of the AHE in tilted Weyl metals by this scheme and found that the side jump contribution exceeds both the intrinsic and skew scattering contribution for the low-energy effective Hamiltonian. We compared the anomalous Hall current obtained from our scheme with the results from the semi-classical Boltzmann equation approach under the relaxation time approximation and found that the results from the two approaches agree with each other in the leading order of the tilting velocity.

References in corpus (19)

• Topological Field Theory of Time-Reversal Invariant Insulators
• Quantized Anomalous Hall Effect in Magnetic Topological Insulators
• High-precision realization of robust quantum anomalous Hall state in a hard ferromagnetic topological insulator
• Quantum Hall Ferromagnetism in Graphene
• Intrinsic vs. extrinsic anomalous Hall effect in ferromagnets
• Anomalous Hall Effect in Weyl Metals
• Chiral anomaly and transport in Weyl metals
• Semiclassical theories of the anomalous Hall effect
• Anomalous Hall effect in 2D Dirac band: link between Kubo-Streda formula and semiclassical Boltzmann equation approach
• Charge and spin Hall conductivity in metallic graphene
• Vertex Corrections on the Anomalous Hall Effect in Spin-polarized Two-dimensional Electron Gases with Rashba Spin-orbit Interaction
• Anomalous Nernst and Thermal Hall Effects in Tilted Weyl Semimetals
• Semiclassical framework for the calculation of transport anisotropies
• Quantum kinetic equation and universal conductance fluctuations in graphene
• Electron-phonon mediated heat flow in disordered graphene
• Transport theory for disordered multiple-band systems: Anomalous Hall effect and anisotropic magnetoresistance
• Anomalous Hall Effect in Disordered Multiband Metals
• Enhanced anomalous Nernst effect in disordered Dirac and Weyl materials
• Sensitivity of anomalous Hall effect to disorder correlations

Cited by in corpus (5)

• Anomalous Hall effect in type-I Weyl metals beyond the noncrossing approximation
• Anomalous Hall effect in disordered Weyl semimetals
• Hall Coulomb drag induced by electron-electron skew scattering
• Strong Field Optical Hall Effect in 2D Weyl Semimetal
• Heat transport in Weyl semimetals in the hydrodynamic regime