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  On the spectral gap in Andreev graphs

Flechsig, H., & Gnutzmann, S. (2008). On the spectral gap in Andreev graphs. In P. Exner, J. P. Keating, P. Kuchment, T. Sunada, & A. Teplyaev (Eds.), Proceedings of Symposia In Pure Mathematics (pp. 381-395). Providence, RI 02940, USA: American Mathematical Society.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-0010-FED3-7 Version Permalink: https://hdl.handle.net/11858/00-001M-0000-0010-FED4-5
Genre: Conference Paper

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0711.1998v1.pdf (Preprint), 442KB
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https://hdl.handle.net/11858/00-001M-0000-0010-FED2-9
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0711.1998v1.pdf
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arXiv:0711.1998v1 [cond-mat.supr-con] 13 Nov 2007
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 Creators:
Flechsig, Holger1, Author           
Gnutzmann, Sven, Author
Affiliations:
1Physical Chemistry, Fritz Haber Institute, Max Planck Society, ou_634546              

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Free keywords: Billiards; statistics
 Abstract: We introduce Andreev scattering (electron-hole conversion at all interface of a normal conductor to a superconductor) at the outer vertices of a quantum star graph and examine its effect on the spectrum. More specifically we show that the density of states in Andreev graphs is suppressed near the Fermi energy where a spectral gap may occur. The size and existence of such a gap depends on one side oil the Andreev scattering amplitudes and, oil the other side, on the properties of the electron-electron scattering matrix at the central vertex. We also show that the bond length fluctuations have a minor effect oil the spectrum near the Fermi energy.

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Language(s): eng - English
 Dates: 2008
 Publication Status: Issued
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: eDoc: 400782
 Degree: -

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Title: Analysis on Graphs and Its Applications Program
Place of Event: Issac Newton Inst Math Sci, Cambridge, UK
Start-/End Date: 2008-01-08 - 2008-06-29

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Title: Proceedings of Symposia In Pure Mathematics
Source Genre: Proceedings
 Creator(s):
Exner, Pavel, Editor
Keating, Jonathan P., Editor
Kuchment, Peter, Editor
Sunada, Toshikazu, Editor
Teplyaev, Alexander, Editor
Affiliations:
-
Publ. Info: Providence, RI 02940, USA : American Mathematical Society
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 381 - 395 Identifier: ISBN: 978-0-8218-4471-7

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Title: Analysis on Graphs and its Applications
Source Genre: Series
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Publ. Info: -
Pages: - Volume / Issue: 77 Sequence Number: - Start / End Page: - Identifier: ISSN: 0082-0717