Many-body fermionic excitations in Weyl semimetals due to elastic gauge fields

We study the single-particle spectrum of three-dimensional Weyl semimetals taking into account electron-phonon interactions that are the result of straining the material. We find that a well-defined fermionic excitation appears in addition to the standard peak corresponding to quasiparticle states as suggested by Landau-Fermi liquid theory. Contrary to the case of Dirac systems interacting via the Coulomb interaction, these satellite peaks appear even at lowest order in perturbation theory. The new excitations are anisotropic, as opposed to the single-particle spectrum, and their behavior is dictated by the Debye frequency, which naturally regulates the electron-phonon coupling.