## Universal Properties of Mesoscopic Fluctuations of the Secondary "Smile" Gap

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2021
Nazarov, Yuli V.
Preprint
Published
##### Abstract
The energy levels of a quasi-continuous 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 the secondary "smile" 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 at al. [Phys. Rev. Lett. \textbf{86}, 874 (2001)] for the distribution of the minigap edge in the opposite limit ETh ≪Δ . 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.
530 Physics
##### Keywords
energy levels, mesoscopic fluctuations, "smile" gap
##### Cite This
ISO 690REUTLINGER, Johannes, Leonid I. GLAZMAN, Yuli V. NAZAROV, Wolfgang BELZIG, 2021. Universal Properties of Mesoscopic Fluctuations of the Secondary "Smile" Gap
BibTex
@unpublished{Reutlinger2021-09-07T12:44:16ZUnive-54837,
year={2021},
title={Universal Properties of Mesoscopic Fluctuations of the Secondary "Smile" Gap},
author={Reutlinger, Johannes and Glazman, Leonid I. and Nazarov, Yuli V. and Belzig, Wolfgang}
}

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<dcterms:abstract xml:lang="eng">The energy levels of a quasi-continuous 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 the secondary "smile" 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 E&lt;sub&gt;Th&lt;/sub&gt; ≫Δ  with E&lt;sub&gt;Th&lt;/sub&gt; 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 Δ&lt;sub&gt;g&lt;/sub&gt; with the value between the level spacing in the cavity δ&lt;sub&gt;s&lt;/sub&gt; and the quasiclassical value of the gap E&lt;sub&gt;g&lt;/sub&gt;. 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 at al. [Phys. Rev. Lett. \textbf{86}, 874 (2001)] for the distribution of the minigap edge in the opposite limit E&lt;sub&gt;Th&lt;/sub&gt; ≪Δ . 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.</dcterms:abstract>
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