# Doubling Theorem and Boundary States of Five-Dimensional Weyl Semimetal

## TL;DR

This paper explores the topological band structures of five-dimensional Weyl semimetals, proving linking constraints of Weyl surfaces and revealing complex boundary states including Fermi hypersurfaces and Weyl arcs.

## Contribution

It generalizes the Doubling Theorem to 5D Weyl semimetals and analyzes the resulting boundary states and topological constraints.

## Key findings

- Weyl surfaces can have nontrivial linkings with second Chern numbers.
- Boundary hosts 3D chiral Fermi hypersurfaces protected by bulk topology.
- Linked Weyl surfaces lead to 1D Weyl nodal arcs on the boundary.

## Abstract

We study the generic band structures of the five-dimensional (5D) Weyl semimetal, in which the band degeneracies are 2D Weyl surfaces in the momentum space, and may have non-trivial linkings with each other if they carry nonzero second Chern numbers. We prove a number of theorems constraining the topological linking configurations of the Weyl surfaces, which can be viewed as a 5D generalization of the celebrated Doubling Theorem for 3D Weyl semimetal. As a direct physical consequence of these constraints, the 5D Weyl semimetal hosts a rich structure of topological boundary states. We show that on the 4D boundary of the 5D Weyl semimetal, there are 3D chiral Fermi hypersurfaces protected by bulk Weyl surfaces. On top of that, for bulk Weyl surfaces that are linked and carry nonzero second Chern numbers, the associated boundary 3D Fermi hypersurfaces will shrink to singularities at certain energies, which trace out a protected 1D Weyl nodal arc, in analogy to the Fermi arc on the 3D Weyl semimetal surface.