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Condensed Matter > Other Condensed Matter

arXiv:2501.11186 (cond-mat)
[Submitted on 19 Jan 2025]

Title:Bulk-edge correspondence in circular-symmetric models

Authors:Klaus Ziegler
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Abstract:We propose a systematic analysis of the eigenfunctions of two-band systems in two dimensions with a circular edge. Our approach is based on an analytic continuation of the wavenumber, which yields a mapping from the bulk modes to the edge modes. Phase relations of the eigenfunctions are described by their mapping onto a three-dimensional field of unit vectors. This mapping is studied in detail for a two-band Laplacian model and a Dirac model. The direction of the unit vector identifies the phase relation of the eigenfunctions and enables us to distinguish between the upper band, the lower band and the edge spectrum. Bulk and edge modes are spectrally separated, which results in two transitions from delocalized bulk modes to localized edge modes. These transitions are accompanied by transitions of the phase relations.
Comments: 12 pages, 5 figures
Subjects: Other Condensed Matter (cond-mat.other); Mathematical Physics (math-ph); Quantum Physics (quant-ph)
Cite as: arXiv:2501.11186 [cond-mat.other]
  (or arXiv:2501.11186v1 [cond-mat.other] for this version)
  https://doi.org/10.48550/arXiv.2501.11186

Submission history

From: Klaus Ziegler [view email]
[v1] Sun, 19 Jan 2025 22:04:50 UTC (640 KB)
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