Non-Abelian Reciprocal Braiding of Weyl Nodes release_wyc6fiw4xjanbfdqjmebqv4654

by Adrien Bouhon, Robert-Jan Slager, Tomáš Bzdušek

Released as a article .

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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Date   2019-07-24
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arXiv  1907.10611v1
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