Topology and interactions in a frustrated slab: tuning from Weyl semi-metal to $C>1$ fractional Chern insulators*

We show that a $[111]$ slab of spin-orbit coupled pyrochlore lattice can become a Weyl semi-metal phase with exotic surface states called as Fermi arcs, i.e., these states are localized to different surfaces depending on their quasi-momentum. Remarkably, in this model, these Fermi arcs persists even when there is no Weyl point in the bulk. Considering interacting electrons in slabs of finite thickness, we find a plethora of known fractional Chern insulating phases, including a new discovered higher Chern number state which is likely a generalization of the Moore-Read fermionic fractional quantum Hall state. By contrast, in the three-dimensional limit, we argue for the absence of gapped states of the flat surface band due to a topologically protected coupling of the surface to gapless states in the bulk. We comment on generalizations as well as experimental perspectives in thin slabs of pyrochlore iridates.