Weyl superconductor phases in a Weyl-semimetal/superconductor multilayer

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.