Science paper proposes non-Abelian band topology

This was published on September 11, 2019

A paper published in the journal Science by NCCR MARVEL's QuanSheng Wu, postdoc in the group of Oleg Yazyev at EPFL, Alexey Soluyanov, professor at the Physics Institute of the University of Zurich as well as group leader in Design & Discovery Project 6, and colleague Tomáš Bzdušek at Stanford University  introduces non-Abelian topological charges that characterize line nodes inside the momentum space of certain symmetric crystalline metals with weak spin-orbit coupling. The analysis goes beyond the standard approach to band topology, and implies the existence of 1D topological phases not present in existing classifications.

Carey Sargent, EPFL

Electron energy bands of crystalline solids generically exhibit degeneracies called band-structure nodes. In a paper to be published in Science on 20 September, MARVEL researchers from EPFL and the University of Zurich as well as a colleague from Stanford University introduce non-Abelian topological charges that characterize line nodes inside the momentum space of certain symmetric crystalline metals with weak spin-orbit coupling.

They show that these are quaternion charges, similar to those describing disclinations in biaxial nematics. Starting from two-band considerations, they developed the complete many-band description of nodes in the presence of certain symmetries, allowing them to investigate the topological stability of nodal chains in metals. The non-Abelian charges put strict constraints on the possible nodal line configurations.

Fig. 1 Nodal lines (NLs) in two-band models.

Their analysis goes beyond the standard approach to band topology, and implies the existence of 1D topological phases not present in existing classifications.

Reference: Non-Abelian band topology in noninteracting metals, by QuanSheng Wu, Alexey A. Soluyanov, Tomáš Bzdušek. Published Online 20 Sep 2019

DOI: 10.1126/science.aau8740

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