Dynamical Effects from Anomaly: Modified Electrodynamics in Weyl Semimetal

Abstract

We discuss the modified quantum electrodynamics from a time-reversal-breaking Weyl semimetal coupled with a $U(1)$ gauge (electromagnetic) field. A key role is played by the soft dispersion of the photons in a particular direction, say $\hat{z}$, due to the Hall conductivity of the Weyl semimetal. Due to the soft photon, the fermion velocity in $\hat{z}$ is logarithmically reduced under renormalization group flow, together with the fine structure constant. Meanwhile, fermions acquire a finite lifetime from spontaneous emission of the soft photon, namely the Cherenkov radiation. At low energy $E$, the inverse of the fermion lifetime scales as ${\tau }^{-1}\sim E/\mathrm{PolyLog}(E)$. Therefore, even though fermion quasiparticles are eventually well-defined at very low energy, over a wide intermediate energy window the Weyl semimetal behaves like a marginal Fermi liquid. Phenomenologically, our results are more relevant for emergent Weyl semimetals, where the fermions and photons all emerge from strongly correlated lattice systems. Possible experimental implications are discussed.

arXiv comment8 pages, 4 figures

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