Print Email Facebook Twitter Universal properties of mesoscopic fluctuations of the secondary gap in superconducting proximity systems Title Universal properties of mesoscopic fluctuations of the secondary gap in superconducting proximity systems Author Reutlinger, J. (Universität Konstanz) Glazman, L. (Yale University) Nazarov, Y.V. (TU Delft QN/Nazarov Group; Kavli institute of nanoscience Delft) Belzig, W (TU Delft QN/Theoretical Physics; Universität Konstanz) Date 2022 Abstract The energy levels of a quasicontinuous spectrum in mesoscopic systems fluctuate in positions and the distribution of the fluctuations reveals information about the microscopic nature of the structure under consideration. Here, we investigate mesoscopic fluctuations of a secondary gap that appears in the quasiclassical spectrum of a chaotic cavity coupled to one or more superconductors. Utilizing a random matrix model, we compute numerically the energies of Andreev levels and access the distribution of the gap widths. We mostly concentrate on the universal regime ETh≫Δ, with ETh being the Thouless energy of the cavity and Δ being the superconducting gap. We find that the distribution is determined by an intermediate energy scale Δg with the value between the level spacing in the cavity δs and the quasiclassical value of the gap Eg. From our numerics we extrapolate the first two cumulants of the gap distribution in the limit of large level and channel number. We find that the scaled distribution in this regime is the Tracy-Widom distribution: the same as found by Vavilov et al. [Phys. Rev. Lett. 86, 874 (2001)0031-900710.1103/PhysRevLett.86.874] for the distribution of the minigap edge in the opposite limit EThΔ. This leads us to the conclusion that the distribution found is a universal property of chaotic proximity systems at the edge of a continuous spectrum in agreement with the known random matrix models featuring a square root singularity in the density of states. To reference this document use: http://resolver.tudelft.nl/uuid:659d7986-bd80-4338-8ddd-6a149ce8dc4d DOI https://doi.org/10.1103/PhysRevB.106.214513 ISSN 2469-9950 Source Physical Review B, 106 (21) Part of collection Institutional Repository Document type journal article Rights © 2022 J. Reutlinger, L. Glazman, Y.V. Nazarov, W Belzig Files PDF PhysRevB.106.214513.pdf 1.7 MB Close viewer /islandora/object/uuid:659d7986-bd80-4338-8ddd-6a149ce8dc4d/datastream/OBJ/view