Weyl-superconductor phases in the multilayer model of Weyl semimetals and superconductors

We study the superconducting proximity effect in the bulk of Weyl semimetals by considering a multilayer structure consisting of alternating Weyl-semimetal and superconductor (WSM-SC) layers. Our model realizes Weyl-superconductor phases with 2 or 4 nodes of the Majorana fermion, and (2d) topological-superconductor phases characterized by half-odd-integer and integer Chern numbers. We found that potential barriers at the interface and/or mismatch of the Fermi velocity favor topological-superconductor phases with half-odd integer Chern numbers, while Weyl-superconductor phases with 4 nodes and topological-superconductor phases with integer Chern numbers are realized when the Fermi velocity coincides. Topological-superconductor phases are characterized by the quantization of the thermal Hall conductivity, and Weyl-superconductor phases by continuously varying thermal Hall conductivity determined by the position of nodes.