Weyl semimetals and superconductors 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 orbital selective superlattice. Such structure breaks mirror symmetry along the superlattice growth axis which, with the help of either a basal plane spin-orbit coupling or a spinless p+ip superconductivity, stabilizes a 3D Dirac node. To explore this idea, we develop a 3D generalization of Haldane model and a Bogoliubov-de-Gennes (BdG) Hamiltonian for the two cases, respectively, and show that a 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 state by violating its particle-hole symmetry but not any other symmetries. Finally, implications of our results for the realization of anomalous Hall effect and Majorana bound state are discussed.