The electronic structure of normal metal–superconductor bilayers

Abstract

We study the electronic properties of ballistic thin normal metal–bulksuperconductor heterojunctions by solving the Bogoliubov–de Gennesequations in the quasiclassical and microscopic ‘exact’ regimes. In particular,the significance of the proximity effect is examined through a series ofself-consistent calculations of the space-dependent pair potential Δ(r).It is found that self-consistency cannot be neglected for normal metallayer widths smaller than the superconducting coherence length ξ0,revealing its importance through discernible features in the subgapdensity of states. Furthermore, the exact self-consistent treatmentyields a proximity-induced gap in the normal metal spectrum, whichvanishes monotonically when the normal metal length exceeds ξ0.Through a careful analysis of the excitation spectra, we find that quasiparticletrajectories with wavevectors oriented mainly along the interface play a criticalrole in the destruction of the energy gap.