Non-Abelian Reciprocal Braiding of Weyl Nodes
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by
Adrien Bouhon, Robert-Jan Slager, Tomáš Bzdušek
2019
Abstract
We illustrate a procedure that defines and converts 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 demonstrate that band
nodes in systems with C_2T symmetry exhibit such braiding properties,
requiring no particular fine-tuning. We further present observables in the form
of generalized Berry phases, calculated via a mathematical object known as
Euler form. We demonstrate our findings with explicit models and a protocol
involving three bands, for which the braid factors mimic quaternion charges.
This protocol is implementable in cold atoms setups and in photonic systems,
where observing the proposed braid factors relates to readily available
experimental techniques. The required C_2T symmetry is also omnipresent in
graphene van-der-Waals heterostructures, which might provide an alternative
route towards realizing the non-Abelian conversion of band nodes.
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