Weyl semimetal and superconductor designed in an orbital-selective superlattice

We propose two complementary design principles for engineering three-dimensional (3D) Weyl semimetals and superconductors in a layer-by-layer setup which includes even-and odd-parity orbitals in alternating layers-dubbed an orbital selective superlattice. Such a structure breaks mirror symmetry along the superlattice growth axis which, with the help of either a basal plane spin-orbit coupling or spinless p + ip superconductivity, stabilizes a 3D Dirac node. To explore this idea, we develop a 3D generalization of the Haldane model and a Bogoliubov-de Gennes Hamiltonian for the two cases, respectively, and show that tunable single or multiple Weyl nodes with linear dispersion in all spatial directions can be engineered desirably in a widespread parameter space. We also demonstrate that a single helical Weyl band can be created at the Gamma point at the Fermi level in the superconducting case via gapping out either of the orbital states by violating its particle-hole symmetry but not any other symmetries. Finally, implications of our results for the realization of an anomalous Hall effect and Majorana bound state are discussed.