Goos-H\"anchen-like shifts at metal/superconductor interface

TL;DR

This paper demonstrates that lateral Goos-H"anchen-like shifts occur at metal/superconductor interfaces during electron and hole reflections, with the shifts depending on energy and material properties, affecting waveguide modes and suggesting experimental detection.

Contribution

It reveals the existence and characteristics of lateral shifts at metal/superconductor interfaces, including their dependence on excitation energy and material specifics like graphene.

Findings

Normal reflection shift can be positive or negative depending on energy.

Andreev reflection shift can be negative, especially in graphene.

Shifts significantly influence waveguide mode dispersion.

Abstract

At a normal-metal/superconductor interface, an incident electron from the normal-metal (N) side can be normally reflected as an electron or Andreev reflected as a hole. We show that pronounced lateral shifts along the interface between the incident and the reflected quasiparticles can happen in both reflection processes, which are analogous to the Goos-H\"anchen effect in optics. Two concrete model systems are considered. For the simplest model in which the N side is of the two-dimensional electron gas, we find that while the shift in Andreev reflection stays positive, the shift in normal reflection can be made either positive or negative, depending on the excitation energy. For the second model with the N side taken by graphene, the shift in Andreev reflection can also be made negative, and the shifts have rich behavior due to the additional sublattice pseudospin degree of freedom. We show that the shift strongly modifies the dispersion for the confined waveguide modes in an SNS structure. We also suggest a possible experimental setup for detecting the shift.