Non-Abelian Reciprocal Braiding of Weyl Nodes and its Manifestation in ZrTe [article]

Adrien Bouhon, QuanSheng Wu, Robert-Jan Slager, Hongming Weng, Oleg V. Yazyev, Tomáš Bzdušek
2020 arXiv   pre-print
We illustrate a procedure that transforms non-Abelian charges of Weyl nodes via braid phase factors, which arise upon exchange inside the reciprocal momentum space. This phenomenon derives from intrinsic symmetry properties of topological materials, which are increasingly becoming available due to recent cataloguing insights. Specifically, we show that band nodes in systems with C_2T symmetry exhibit such braiding properties, requiring no particular fine-tuning, and we present observables in
more » ... form of generalized Berry phases, calculated via a mathematical object known as Euler form. We further extend the notion of non-Abelian topology to C_2T-symmetric systems in three spatial dimensions, and investigate the interplay with the additional point-group symmetry. We find that the interaction of Euler class with mirror symmetry governs non-trivial conversions between Weyl points and nodal lines. While our findings are directly implementable in cold-atoms setups and in photonic systems via a presented braiding protocol, the predictive power of our framework is firmly underpinned by tangible material identification, namely zirconium telluride (ZrTe), which we predict to exhibit the aforementioned conversion effect under uniaxial compression strain.
arXiv:1907.10611v3 fatcat:m6kkmqlfsne6jfjtqs7phwx45y