Andreev reflection and the semiclassical Bogoliubov-de Gennes Hamiltonian: Resonant states

Amira Bensouissi (1, 2, 3) , Abdelwahe Ifa (1, 2, 3) , Michel L. Rouleux (1, 3)

1 CPT - Centre de Physique Théorique - UMR 6207
2 Département de mathématiques [Tunis]
3 CPT - Centre de Physique Théorique - UMR 7332

We present a semi-classical analysis of the opening of superchannels in gated mesoscopic SNS junctions. For perfect junctions (i.e. hard-wall potential), this was considered by [ChLeBl] in the framework of scattering matrices. Here we allow for imperfections in the junction, so that the complex order parameter continues as a smooth function, which is a constant in the superconducting banks, and vanishes rapidly inside the lead. We obtain quantization rules for resonant Andreev states near energy E close to the Fermi level, including the determination of the resonance width.

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]

Amira Bensouissi, Abdelwahe Ifa, Michel L. Rouleux. Andreev reflection and the semiclassical Bogoliubov-de Gennes Hamiltonian: Resonant states . Days on Diffraction 2011, May 2011, St. Petersburg Russia. pp.39-44, ⟨10.1109/DD.2011.6094362⟩. ⟨hal-00439616⟩