On the spectral gap in Andreev graphs

Holger Flechsig; Sven Gnutzmann

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arXiv · 0711.1998

On the spectral gap in Andreev graphs

Holger Flechsig·Sven Gnutzmann

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Abstract

We introduce Andreev scattering (electron-hole conversion at an 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 on the Andreev scattering amplitudes and, on 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 on the spectrum near the Fermi energy.

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Holger Flechsig, Sven Gnutzmann. 2007-11-13. On the spectral gap in Andreev graphs. https://arxiv.org/abs/0711.1998

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