# Weyl Semimetal and Topological Phase Transition in Five Dimensions

## TL;DR

This paper explores five-dimensional Weyl semimetals with Yang monopoles and Weyl surfaces, analyzing their topological properties and phase transitions, revealing how symmetry breaking leads to linked Weyl structures and intermediate semimetal phases.

## Contribution

It introduces 5d Weyl semimetals with Yang monopoles and linked Weyl surfaces, and studies their topological phase transitions and symmetry-breaking effects.

## Key findings

- Yang monopoles reduce to Hopf links when symmetry is broken
- 5d Weyl semimetals appear as intermediate phases in topological transitions
- Linked Weyl surfaces carry the second Chern number as a topological invariant

## Abstract

We study two Weyl semimetal generalizations in five dimensions (5d) which have Yang monopoles and linked Weyl surfaces in the Brillouin zone, respectively, and carry the second Chern number as a topological number. In particular, we show a Yang monopole naturally reduces to a Hopf link of two Weyl surfaces when the $\mathbf{TP}$ (time-reversal combined with space-inversion) symmetry is broken. We then examine the phase transition between insulators with different topological numbers in 5d. In analogy to the 3d case, 5d Weyl semimetals emerge as intermediate phases during the topological phase transition.