  Two common approaches of studying theoretically the property of a
superconductor are shown to have significant differences, when they are applied
to the Larkin-Ovchinnikov state of Weyl metals. In the first approach the
pairing term is restricted by a cutoff energy to the neighborhood of the Fermi
surface, whereas in the second approach the pairing term is extended to the
whole Brillouin zone. We explore their difference by considering two minimal
models for the Weyl metal. For a model giving a single pair of Weyl pockets,
both two approaches give a partly-gapped (fully-gapped) bulk spectrum for small
(large) pairing amplitude. However, for very small cutoff energy, a portion of
the Fermi surface can be completely unaffected by the pairing term in the first
approach. For the other model giving two pairs of Weyl pockets, while the bulk
spectrum for the first approach can be fully gapped, the one from the second
approach has a robust line node, and the surface states are also changed
qualitatively by the pairing. We elucidate the above differences by topological
arguments and analytical analyses. A factor common to both of the two models is
the tilting of the Weyl cones which leads to asymmetric normal state band
structure with respect to the Weyl nodes. For the Weyl metal with two pairs of
Weyl pockets, the band folding leads to a double degeneracy in the effective
model, which distinguishes the pairing of the second approach from all others.

Superconductivity