Sticky Goos-Hänchen effect at normal/superconductor interface

We study the quantum Goos-Hänchen (GH) effect for wave-packet dynamics at a normal/superconductor (NS) interface. We find that the effect is amplified by a factor , with EF the Fermi energy and Δ the gap. Interestingly, the GH effect appears only as a time delay without any lateral shift, and the corresponding delay length is about , with the Fermi wavelength. This makes the NS interface "sticky" when , since typically GH effects are of wavelength order. This "sticky" behavior can be further enhanced by a resonance mode in the NSNS interface. Finally, for a large Δ, the resonance-mode effect makes a transition from the Andreev to the specular reflection as the width of the sandwiched superconductor is reduced.