Fu–Kane–Mele monopoles in semimetals

In semimetals with time-reversal symmetry, the interplay between Weyl points and Fu–Kane–Mele indices results in coexisting surface Dirac cones and Fermi arcs that are transmutable without a topological phase transition. We show that Weyl points act as a new type of monopole, and that their connectivity is essential for capturing the full topology of semimetals and their role as intermediaries of topological insulator transitions. The history of Weyl point creation–annihilation provides a simple and mathematically equivalent way to classify semimetals, and directly prefigures the surface state topology. We further predict the possibility of a topological Dirac cone on the interface between two Weyl semimetals.