Charge-spin response and collective excitations in Weyl semimetals*

We present analytical expressions for all components of the frequency- and wave-vector-dependent charge-spin
linear-response tensor of Weyl fermions. The spin-momentum locking of the Weyl Hamiltonian
leads to a coupling between charge and longitudinal spin fluctuations, while transverse spin fluctua-
tions remain decoupled from the charge. Based on the response tensor, we investigate the low-energy
collective excitations of interacting Weyl fermions. For a local Hubbard interaction, the charge-spin
coupling leads to a dramatic change of the zero-sound dispersion: its velocity becomes independent
of the interaction strength and the chemical potential and is given solely by the Fermi velocity. In
the presence of long-range Coulomb interactions, the coupling transforms the plasmon modes into
spin plasmons. Using a lattice model with two Weyl nodes, we show that the collective modes are
strongly affected by the presence of parallel static electric and magnetic fields due to the chiral
anomaly. We discuss possible experiments that could
provide smoking-gun evidence of Weyl physics.