Electromagnetic response of interacting Weyl semimetals

Abstract

We study the electromagnetic properties of Weyl semimetals with strong interactions. Focusing on a single Weyl cone in the band structure, we induce strong interactions by coupling the Weyl fermion with a tunable coupling constant $g_f$ to a quantum critical system. The critical fluctuations are described by a conformal field theory containing fermionic operators with scaling dimension $\Delta$. Employing the methods of the holographic correspondence, we then derive the effective theory of the Weyl fermion in the presence of external electric and magnetic fields. In particular, we determine the frequency and momentum-dependent anomalous magnetic moment of the Weyl fermions. We also determine the conductivity of the Weyl semimetal including the vertex corrections consistent with the Ward identity. Finally, we connect our construction to the case of Coulomb interactions in Weyl semimetals by tuning the parameters $\Delta \to 5/2$ and $g_f^2 \rightarrow e/\sqrt{\hbar cε_0$.

5 pages, 4 figures: v2 presentation improved, typos corrected

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• A smeared quantum phase transition in disordered holography
• Illustrated study of the semi-holographic non-perturbative framework
• Thermodynamics and transport of holographic nodal line semimetals
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• Reentrant Metallic Behavior in the Weyl Semimetal NbP
• Large anomalous magnetic moment in three-dimensional Dirac and Weyl semimetals
• Momentum relaxation of holographic Weyl semimetal from massive gravity
• Topological characteristics of gap closing points in nonlinear Weyl semimetals
• Nonrelativistic fermions with holographic interactions and the unitary Fermi gas