Xuzhe Ying

Abstract It has recently been demonstrated that it is possible to open a gap in a magnetic Weyl semimetal, while preserving the chiral anomaly along with the charge conservation and translational symmetries, which all protect the gapless nodes in a weakly interacting semimetal. The resulting state was shown to be a nontrivial generalization of a non-Abelian fractional quantum Hall liquid to three dimensions. Here we point out that a second fractional quantum Hall state exists in this case.

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 ẑ, due to the Hall conductivity of the Weyl semimetal. Due to the soft photon, the fermion velocity in ẑ is logarithmically reduced under renormalization group flow, together with the fine-structure constant.

Abstract Luttinger's theorem connects a basic microscopic property of a given metallic crystalline material, the number of electrons per unit cell, to the volume, enclosed by its Fermi surface, which defines its low-energy observable properties. Such statements are valuable since, in general, deducing a low-energy description from microscopics, which may perhaps be regarded as the main problem of condensed matter theory, is far from easy.