Enhanced Andreev Reflection in Flat-Band Systems: Wave Packet Dynamics, DC Transport and the Josephson Effect

TL;DR

This paper studies how flat bands in an extended $ ext{alpha-} ext{T}_3$ lattice enhance Andreev reflection and induce Hall-like effects in Josephson junctions, combining wave packet dynamics with transport analysis.

Contribution

It reveals the significant enhancement of Andreev reflection due to flat bands and uncovers directional asymmetry and Hall-like responses in Josephson junctions within this lattice.

Findings

Flat bands significantly enhance Andreev reflection.

Band flatness and anisotropic dispersion induce Goos-H"anchen shifts.

Transport in SNS junctions exhibits Hall-like responses due to flat bands.

Abstract

We investigate Andreev reflection (AR) in a proximity-induced normal-superconductor (NS) junction within the extended $\alpha-\mathcal{T}_3$ lattice, emphasizing the impact of flat bands on AR. Our findings reveal that flat bands significantly enhance AR. Through wave packet dynamics, we track the real-time evolution of quasi-particle wave packets across the junction, providing deeper insight into electron-hole conversion. Notably, the combination of band flatness and anisotropic dispersion in the $k_x-k_y$ plane induces an electronic analog of Goos-H\"anchen (GH) shifts at the NS interface, exhibiting directional asymmetry along the junction. This asymmetry leads to a Hall-like response in Josephson junction in SNS geometry, where transport across the junction region is dominated by the quasi-flat bands.