Dynamical effects from anomalies: Modified electrodynamics in Weyl semimetals

Abstract

Here, 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 τ -1 ~E/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.