Non-Abelian braiding of Weyl nodes via symmetry-constrained phase transitions

Weyl semimetals are arguably the most paradigmatic form of a gapless topological phase. While the stability of Weyl nodes, as quantified by their topological charge, has been extensively investigated, recent interest has shifted to the manipulation of the location of these Weyl nodes for non-Abelian braiding. To accomplish this braiding it is necessary to drive significant Weyl node motion using realistic experimental parameter changes. We show that a family of phase transitions characterized by certain symmetry constraints impose that the Weyl nodes have to reorganize by a large amount, shifting from one high-symmetry plane to another. Additionally, for a subset of pairs of nodes with nontrivial Euler class topology, this reorganization can only occur through a braiding process with adjacent nodes. As a result, the Weyl nodes are forced to move a large distance across the Brillouin zone and to braid, all driven by small temperature changes, a process we illustrate with Cd2Re2O7.

Automated summary

Weyl semimetals have been studied extensively, and recent research focuses on manipulating the location of Weyl nodes for non-Abelian braiding. A certain type of phase transition imposes a significant reorganization of Weyl nodes, particularly for pairs of nodes with nontrivial topology, which can only be achieved through braiding with adjacent nodes. This motion and braiding process can be driven by small temperature changes.