Collective Modes Of Weyl Fermions With Repulsive S-Wave Interaction*

We calculate the spin and density susceptibility of Weyl fermions with repulsive S-wave interaction in ultracold gases. Weyl fermions have a linear dispersion, which is qualitatively different from the parabolic dispersion of conventional materials. We find that there are different collective modes for the different strengths of repulsive interaction by solving the poles equations of the susceptibility in the random-phase approximation. In the long-wavelength limit, the sound velocity and the energy gaps vary with the different strengths of the interaction in the zero sound mode and the gapped modes, respectively. The particle-hole continuum is obtained as well, where the imaginary part of the susceptibility is nonzero.