Five-dimensional generalization of the topological Weyl semimetal

Biao Lian, Shou Cheng Zhang

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48 Scopus citations


We generalize the concept of three-dimensional topological Weyl semimetals to a class of five dimensional (5D) gapless solids, where Weyl points are generalized to Weyl surfaces which are two-dimensional closed manifolds in the momentum space. Each Weyl surface is characterized by a U(1) second Chern number C2 defined on a four-dimensional manifold enclosing the Weyl surface, which is equal to its topological linking number with other Weyl surfaces in 5D. In analogy to the Weyl semimetals, the surface states of the 5D metal take the form of topologically protected Weyl fermion arcs, which connect the projections of the bulk Weyl surfaces. The further generalization of topological metals in 2n+1 dimensions carrying the nth Chern number Cn is also discussed.

Original languageEnglish (US)
Article number041105
JournalPhysical Review B
Issue number4
StatePublished - Jul 5 2016
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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