Axionic field theory of (3+1)-dimensional Weyl semimetals

By P. Goswami, S. Tewari. 2012

257 citations recorded by the source corpus.

From a direct calculation of the anomalous Hall conductivity and an effective electromagnetic action obtained via Fujikawa's chiral rotation technique, we conclude that an axionic field theory with a nonquantized coefficient describes the electromagnetic response of the $(3+1)$-dimensional Weyl semimetal. The coefficient is proportional to the momentum space separation of the Weyl nodes. Akin to the Chern-Simons field theory of quantum Hall effect, the axion field theory violates gauge invariance in the presence of the boundary, which is cured by the chiral anomaly of the surface states via the Callan-Harvey mechanism. This provides a unique solution for the radiatively induced CPT-odd term in the electromagnetic polarization tensor of the Lorentz violating spinor electrodynamics, where the source of the Lorentz violation is a constant axial 4-vector term for the Dirac fermion. A direct linear response calculation also establishes anomalous thermal Hall effect and a Wiedemann-Franz law, but thermal Hall conductivity does not directly follow from the well known formula for the gravitational chiral anomaly.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/bdcf0939c3a05184f292b1380a792a15a2baa4ec

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Citations in the corpus

Inhomogeneous Weyl and Dirac Semimetals: Transport in Axial Magnetic Fields and Fermi Arc Surface States from Pseudo-Landau Levels (2016, background): “[16] Pallab Goswami and Sumanta Tewari, “Axionic field theory of (3+1)-dimensional Weyl semimetals,” Phys.”
Light control with Weyl semimetals (2022, methodology): “In condensed matter physics, axion electrodynamics is used to understand the properties of (3)He [80], topological insulators [81, 82, 83, 68], and Weyl semimetals [74, 84, 85, 86].”
Notes on Anomaly Induced Transport (2016, background): “Another effect present in in our simple model is the quantum anomalous Hall effect [79, 80, 81].”
Weyl and Dirac semimetals in three-dimensional solids (2017, background): “Both CME and the anomalous Hall effect in WSMs can be represented compactly by the addition of the so-called axion term to the electromagnetic Lagrangian (Goswami and Tewari, 2013; Grushin, 2012; Son and Yamamoto, 2012; Vazifeh and Franz, 2013a; Zyuzin and Burkov, 2012; Zyuzin et al., 2012).”