  Topologically nontrivial superconducting phases have been engineered in
topological materials by the proximity effect in contact with conventional
superconductors. In this paper, by using the method of the Kronig-Penney model,
we study the superconducting proximity effect in the bulk electronic states of
Weyl semimetals by considering a multilayer structure consisting of
Weyl-semimetal and superconductor layers. Due to the proximity effect, two Weyl
nodes are decoupled into four nodes of Majorana fermions resulting in
Weyl-superconductor phases or three-dimensional extension of
topological-superconductor phases. We find that mismatch of the Fermi velocity
and potential barriers at the interface gap out Majorana nodes, thus turn
Weyl-superconductor phases with four Majorana nodes into Weyl-superconductor
phases with half of Majorana nodes and topological-superconductor phases with
odd integer Chern numbers.
