  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 $\omega =k_x
k_y$ dispersion. The intrinsically 2D rank-2 chiral fermions have a mixed
charge-momentum anomaly which is cancelled by the bulk of the 3D system.
