Collective modes of type-II Weyl fermions with repulsive S-wave interaction

Three-dimensional type-II Weyl fermions possess overtilted cone-like low-energy band dispersion. Unlike the closed ellipsoidal Fermi surface for type-I Weyl fermions, the Fermi surface is an open hyperboloid for type-II Weyl fermions. We evaluate the spin and density susceptibility of type-II Weyl fermions with repulsive S-wave interaction by means of Green's functions. We obtain the particle-hole continuum along the tilted momentum direction and perpendicular to the tilted momentum direction respectively. We find the zero sound mode in some repulsive interaction strengths by numerically solving the pole equations of the susceptibility within the random-phase approximation.