Manipulation and braiding of Weyl nodes using symmetry-constrained phase transitions

Abstract

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.

7+4 pages; 3+4 figures

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• Successive spatial symmetry breaking under high pressure in the spin-orbit-coupled metal Cd2Re2O7

Cited by in corpus (25)

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• Optical manifestations and bounds of topological Euler class
• Phase transitions of non-Abelian charged nodal links in a spring-mass system
• Landau Levels of the Euler Class Topology
• Interferometry of non-Abelian band singularities and Euler class topology
• Three-dimensional $\mathcal{P}\mathcal{T}$-symmetric topological phases with Pontryagin index
• Disorder-induced topological quantum phase transitions in multi-gap Euler semimetals
• Fermi-arc metals
• Anyonic Topological Order in Twisted Equivariant Differential (TED) K-Theory
• Projected spin texture as a bulk indicator of fragile topology
• Andreev reflection in Euler materials
• Observing the nodal-line conversion determined by the relative homotopy
• Berry curvature inside parity-time-symmetry protected exceptional surface
• Coexisting Euler and Stiefel-Whitney Topological Phases in Elastic Metamaterials
• Floquet non-Abelian topological charges and edge states
• Second Euler number in four dimensional synthetic matter
• Stability of Weyl node merging processes under symmetry constraints
• High-chirality and multiquaternion Weyl nodes in hexagonal ReO${}_3$
• Anomalous multi-gap topological phases in periodically driven quantum rotors
• Euler band topology in superfluids and superconductors
• Probing emergent axion electrodynamics with waveguide apparatus
• Three-dimensional spinless Euler insulators with rotational symmetry
• Gapped spinful phases obtained via Gutzwiller projections of Euler states
• Hinge modes of three-dimensional Euler insulators