Superconducting proximity effect and Majorana flat bands in the surface of a Weyl semimetal

We study the proximity effect between an s-wave superconductor (SC) and the surface states of a Weyl semimetal. An interesting two-dimensional SC forms in such an interface with properties resembling in certain aspects the Fu-Kane superconductor with some notable differences. In a Weyl semimetal with unbroken time reversal symmetry the interface SC supports completely flat Majorana bands in a linear Josephson junction with a {\pi} phase difference. We discuss stability of these bands against disorder and propose ways in which they can be observed experimentally.