On the spectral gap in Andreev graphs

Flechsig, Holger; Gnutzmann, Sven

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On the spectral gap in Andreev graphs

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Flechsig, Holger
Physical Chemistry, Fritz Haber Institute, Max Planck Society;

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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.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0010-FED3-7

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.