Please use this identifier to cite or link to this item: https://hdl.handle.net/2440/109219
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Type: Journal article
Title: Differential topology of semimetals
Author: Varghese, M.
Thiang, G.
Citation: Communications in Mathematical Physics, 2017; 355(2):561-602
Publisher: Springer
Issue Date: 2017
ISSN: 0010-3616
1432-0916
Statement of
Responsibility: 
Varghese Mathai, Guo Chuan Thiang
Abstract: The subtle interplay between local and global charges for topological semimetals exactly parallels that for singular vector fields. Part of this story is the relationship between cohomological semimetal invariants, Euler structures, and ambiguities in the connections between Weyl points. Dually, a topological semimetal can be represented by Euler chains from which its surface Fermi arc connectivity can be deduced. These dual pictures, and the link to topological invariants of insulators, are organised using geometric exact sequences. We go beyond Dirac-type Hamiltonians and introduce new classes of semimetals whose local charges are subtle Atiyah–Dupont–Thomas invariants globally constrained by the Kervaire semicharacteristic, leading to the prediction of torsion Fermi arcs.
Rights: © Springer-Verlag GmbH Germany 2017
DOI: 10.1007/s00220-017-2965-z
Grant ID: http://purl.org/au-research/grants/arc/DP150100008
http://purl.org/au-research/grants/arc/DE170100149
Published version: https://link.springer.com/journal/220
Appears in Collections:Aurora harvest 8
Mathematical Sciences publications

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