Weyl semimetal and topological phase transition in five dimensions

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 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 three-dimensional case, 5D Weyl semimetals emerge as intermediate phases during the topological phase transition.