Quantum mechanics

Conformal symmetry

Theoretical physics

Pure mathematics

Materials science

Phase transition

Node (physics)

Abelian group

Band gap

Physics

Brillouin zone

Mathematics

Semimetal

Geometry

Composite material

Conformal map

Combinatorics

Weyl transformation

Braid

Symmetry (geometry)

Topology (electrical circuits)

Weyl semimetal

Physical review. B./Physical review. B

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 reorganise 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 Cd$_2$Re$_2$O$_7$. Our work opens up routes to readily manipulate Weyl nodes using only slight external parameter changes, paving the way for the practical realization of reciprocal space braiding.

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