We study superconducting states of doped inversion-symmetric Weyl semimetals. Specifically, we consider a lattice model realizing a Weyl semimetal with an inversion symmetry and study the superconducting instability in the presence of a short-ranged attractive interaction. With a phonon-mediated attractive interaction, we find two competing states: a fully gapped finite-momentum Fulde-Ferrell-Larkin-Ovchinnikov pairing state and a nodal even-parity pairing state. We show that, in a BCS-type approximation, the finite-momentum pairing state is energetically favored over the usual even-parity paired state and is robust against weak disorder. Although energetically unfavorable, the even-parity pairing state provides an electronic analog of the ${}^3$He-$A$ phase in that the nodes of the even-parity state carry nontrivial winding numbers and therefore support a surface flat band. We briefly discuss other possible superconducting states that may be realized in Weyl semimetals.

• Received 15 September 2012

DOI:https://doi.org/10.1103/PhysRevB.86.214514