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After a Weyl

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After a Weyl
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Weyl points are the key to non-trivial topological phenomena in 3D. I will give several examples: 1) Two Weyl points of same first Chern number form double-weyl points. Examples of double-weyl phonons will be shown in crystalline solids. 2) Two Weyl points of opposite first Chern number form 3D Dirac points. Glide-symmetry protected gapped phase with a single surface Dirac cone can be obtained by gapping 3D Dirac points. It has a Z2 invariant. 3) A Chern crystal of a full 3D gap can be obtained by gapping a Weyl pair. It is characterized by three first Chern numbers. 4) Coupling two Weyl points with helical modulations provides one-way fibers of second Chern number in 4D parameter space.