Geometrically protected triple-point crossings in an optical lattice

Abstract

We show how to realize topologically protected crossings of three energy bands, integer-spin analogs of Weyl fermions, in three-dimensional optical lattices. Our proposal only involves ultracold atom techniques that have already been experimentally demonstrated and leads to isolated triple-point crossings (TPCs) which are required to exist by a novel combination of lattice symmetries. The symmetries also allow for a new type of topological object, the type-II, or tilted, TPC. Our Rapid Communication shows that spin-1 Weyl points, which have not yet been observed in the bandstructure of crystals, are within reach of ultracold atom experiments.

5 pages, 2 figures + 3 pages, 3 figures supplemental material. Added appendix on model symmetries, fixed typos and added references. This is the final, published version