Winding vectors of topological defects: multiband Chern numbers

  • Chern numbers can be calculated within a frame of vortex fields related to phase conventions of a wave function. In a band protected by gaps the Chern number is equivalent to the total number of flux carrying vortices. In the presence of topological defects like Dirac cones this method becomes problematic, in particular if they lack a well-defined winding number. We develop a scheme to include topological defects into the vortex field frame. A winding number is determined by the behavior of the phase in reciprocal space when encircling the defect's contact point. To address the possible lack of a winding number we utilize a more general concept of winding vectors. We demonstrate the usefulness of this ansatz on Dirac cones generated from bands of the Hofstadter model.

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Author:Axel FünfhausORCiD, Thilo KoppORCiDGND, Elias LettlORCiD
URN:urn:nbn:de:hebis:30:3-860117
DOI:https://doi.org/10.1088/1751-8121/ac8ef7
ISSN:1751-8121
ArXiv Id:http://arxiv.org/abs/2205.01406
Parent Title (English):Journal of physics. A, Mathematical and theoretical
Publisher:IOP Publishing
Place of publication:Bristol
Document Type:Article
Language:English
Date of Publication (online):2022/09/22
Date of first Publication:2022/09/22
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2024/07/01
Volume:55.2022
Issue:40, 405202
Article Number:405202
Page Number:23
Institutes:Physik / Physik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
Sammlungen:Universitätspublikationen
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International