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    Quantum-Size Effect Induced Andreev Bound States in Ultrathin Metallic Islands Proximitized by a Superconductor

    Guanyong Wang1,2,*, Li-Shuo Liu3,*, Zhen Zhu1, Yue Zheng3, Bo Yang1, Dandan Guan1, Shiyong Wang1, Yaoyi Li1, Canhua Liu1 et al.

    Wei Chen3, Hao Zheng1,†, and Jinfeng Jia1,4,5,‡

    • *These authors contributed equally to this work.
    • †Contact author: haozheng1@sjtu.edu.cn
    • ‡Contact author: jfjia@sjtu.edu.cn

    Phys. Rev. Lett. 135, 076201 – Published 11 August, 2025

    DOI: https://doi.org/10.1103/4mw4-4rfh

    Abstract

    While Andreev bound states (ABSs) have been realized in engineered superconducting junctions, their direct observation in normal metal-superconductor heterostructures—enabled by quantum confinement—remains experimentally elusive. Here, we report the detection of ABSs in ultrathin metallic islands (Bi, Ag, and SnTe) grown on the s-wave superconductor NbN. Using high-resolution scanning tunneling microscopy and spectroscopy, we clearly reveal in-gap ABSs with energies symmetric about the Fermi level. While the energies of these states show no position dependence, their wave functions exhibit spatial oscillations, demonstrating a quantum size effect. Both the energy levels and spatial distribution of the ABSs can be reproduced by our effective model in which a metallic island is coupled to the superconducting substrate via the proximity effect. We demonstrate that the coupling strength plays a critical role in determining the ABS energies. Our work introduces a novel physical platform for implementing ABSs, which hold promise for significant device applications.

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