Weyl nodes in periodic structures of superconductors and spin active materials

Motivated by recent progress in epitaxial growth of proximity structures of s-wave superconductors (S) and spin-active materials (M), we show that the periodic structure of S and M can behave effectively as a superconductor with pairs of point nodes, near which the low energy excitations are Weyl fermions. A simple toy model, where M is described by a Kronig-Penney potential with both spin-orbit coupling and exchange field, is proposed and solved to obtain the phase diagram of the nodal structure, the spin texture of the Weyl fermions, as well as the zero energy surface states in the form of open Fermi lines ("Fermi arcs"). Going beyond the simple model, a lattice model with alternating layers of S and magnetic $Z_2$ topological insulators (M) is solved. The calculated spectrum confirms previous prediction of Weyl nodes based on tunneling Hamiltonian of Dirac electrons. Our results provide further evidence that periodic structures of S and M are well suited for engineering gapless topological superconductors.