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

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• Spin-1 Topological Monopoles in Parameter Space of Ultracold Atoms
• Viscous Maxwell-Chern-Simons theory for topological electromagnetic phases of matter
• Chirality flip of Weyl nodes and its manifestation in strained MoTe${}_2$
• Coexistence of spin-1 fermion and Dirac fermion on the triangular kagome lattice
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• Observation of spin-tensor induced topological phase transitions of triply degenerate points with a trapped ion
• Topological van Hove singularities at phase transitions in Weyl metals
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• Disorder effects on triple-point fermions
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• Triply-degenerate point in three-dimensional spinless systems
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