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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Metadaten
Author:Axel FünfhausORCiD, Thilo KoppORCiDGND, Elias LettlORCiD
URN:urn:nbn:de:hebis:30:3-860193
URL:https://arxiv.org/abs/2205.01406v1
DOI:https://doi.org/https://doi.org/10.48550/arXiv.2205.01406
ArXiv Id:http://arxiv.org/abs/2205.01406
Parent Title (English):arXiv
Publisher:arXiv
Document Type:Preprint
Language:English
Date of Publication (online):2022/05/03
Date of first Publication:2022/05/03
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2024/07/01
Issue:2205.01406v1
Edition:Version 1
Page Number:14
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