Sticky Normal-Superconductor Interface

TL;DR

This paper investigates the quantum Goos-Hänchen effect at a normal-superconductor interface, revealing a significant time delay without lateral shift, leading to a 'sticky' interface behavior especially when the superconducting gap is small.

Contribution

It introduces the amplification of the GH effect at NS interfaces and describes the conditions under which the interface becomes 'sticky' due to this effect, including resonance mode influences.

Findings

GH effect amplified by factor (E_F/Δ)

GH effect manifests as a time delay without lateral shift

Resonance modes enhance the 'sticky' behavior

Abstract

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