Superconductivity in doped inversion-symmetric Weyl semimetals

We study theoretically the superconductivity in doped Weyl semimetals with an inversion symmetry based on the Bogoliubov-de Gennes equations. In principle, the two superconducting states, i.e., the zero momentum BCS-like pairing and the finite momentum Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing, are competing in this kind of systems. From the self-consistent calculation and the free-energy analysis, we propose that the BCS-type state may be the ground state. The competition between these two pairing states is studied in detail through normal state Fermi surface and the finite-energy spectral functions. We also study the physical properties and address the Majorana Fermions excitation in these two superconducting states, respectively.