A Five Dimensional Generalization of the Topological Weyl Semimetal

TL;DR

This paper extends the concept of topological Weyl semimetals from three to five dimensions, introducing Weyl surfaces characterized by second Chern numbers and exploring their surface states and higher-dimensional generalizations.

Contribution

It introduces a five-dimensional topological semimetal model with Weyl surfaces and characterizes their topology using second Chern numbers, expanding the theoretical framework of topological metals.

Findings

Weyl points are generalized to Weyl surfaces in 5D.

Weyl surfaces are characterized by second Chern numbers.

Surface states form topologically protected Weyl fermion arcs.

Abstract

We generalize the concept of three-dimensional topological Weyl semimetal 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 $C_2$ 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 metal in $2n+1$ dimensions carrying the $n$-th Chern number $C_n$ is also discussed.