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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. Our self-consistent calculation indicates 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. Generally, the Fermi surface topology supports the FFLO pairing while the finite energy band structure favors the BCS-type pairing. We also study the physical properties and address the Majorana Fermions excitation in these two superconducting state respectively.