We report on exotic response properties in 3D time-reversal invariant Weyl semimetals with mirror symmetry. Despite having a vanishing anomalous Hall coefficient, we find that the momentum-space quadrupole moment formed by four Weyl nodes determines the coefficient of a mixed \emph{electromagnetic charge-stress} response, in which momentum flows perpendicular to an applied electric field, and electric charge accumulates on certain types of lattice defects. This response is described by a mixed Chern-Simons-like term in 3 spatial dimensions, which couples a rank-2 gauge field to the usual electromagnetic gauge field. On certain 2D surfaces of the bulk 3D Weyl semimetal, we find what we will call rank-2 chiral fermions, with ω=kxky dispersion. The intrinsically 2D rank-2 chiral fermions have a mixed charge-momentum anomaly which is cancelled by the bulk of the 3D system.
@article{arxiv.2102.08959,
title = {Higher Rank Chiral Fermions in 3D Weyl Semimetals},
author = {Oleg Dubinkin and F. J. Burnell and Taylor L. Hughes},
journal= {arXiv preprint arXiv:2102.08959},
year = {2021}
}