Absence of the FFLO/BCS hybrid paired ground state in superconducting Weyl semimetals

We study microscopic pairing mechanisms of superconductivity in doped Weyl semimetals. Depending on the nature of the election scattering, there exist three possible superconducting pairings. We evaluate the condensation energy required for electrons to pair up. The ground state of superconducting Weyl semimetals is determined by the fermionic interaction. The scattering between two Weyl nodes plays an important role in pairing mechanisms. It is shown that the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase is the ground state if the electron scattering is dominated by the intranode scattering. On the other hand, if the internode scattering is strong, the ground state is with the BCS pairing. More importantly, we show that the state with FFLO/BCS hybrid pairing cannot be the ground state of superconducting Weyl semimetals, thus our result provides a definitive answer to an unresolved question.