Dynamical Effects from Anomaly: Modified Electrodynamics in Weyl Semimetal

Weyl semimetals (WSM), being a topological gapless phase of matter, show various intriguing features, among which are the chiral anomaly and the Hall effect. In this talk, we discuss the chiral anomaly's impact on the infrared properties of a strongly interacting Weyl semimetal.

At the mean-field level, a strongly interacting Weyl semimetal is described as 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 z-direction, due to the Hall conductivity of the Weyl semimetal. Due to the soft photon, the fermion velocity in the z-direction 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.