On the spectral gap in Andreev graphs

zbMATH Open1155.81333arXiv0711.1998MaRDI QIDQ3545443

Publication date: 10 December 2008

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.

Full work available at URL: https://arxiv.org/abs/0711.1998

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Quantum chaos (81Q50) Eigenvalues, singular values, and eigenvectors (15A18) Statistical mechanics of superconductors (82D55) (2)-body potential quantum scattering theory (81U05) Boundary value problems on graphs and networks for ordinary differential equations (34B45)

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