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 quasiparticle wave packets across the junction, providing deeper insight into electron-hole conversion. Notably, the combination of band flatness and anisotropic dispersion in the $k_x\text{−}{k}_y$ plane induces an electronic analog of Goos-Hänchen (GH) shifts at the NS interface, exhibiting directional asymmetry along the junction. This asymmetry leads to a Hall-like response in a Josephson junction in the superconductor–normal-metal–superconductor geometry, where transport across the junction region is dominated by the quasiflat bands.

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• Andreev reflection
• Critical current
• Density of states
• Flat bands
• Superconductivity
• Josephson junctions
• Landauer formula