Abundance of Weyl points in semiclassical multi-terminal superconducting nanostructures

Barakov, Hristo; Nazarov, Yuli V.

doi:10.48550/arxiv.2112.13928

Cited by 2 publications

(3 citation statements)

References 44 publications

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“…In this limit, the whole subgap density of states has a universal shape not depending on E Th . Similar finite-energy gap structures have been found in the multiterminal junction and could be related to topological properties [20,21].…”

Section: Introductionsupporting

confidence: 77%

Universal properties of mesoscopic fluctuations of the secondary gap in superconducting proximity systems

et al. 2022

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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 E Th, with E Th being the Thouless energy of the cavity and being the superconducting gap. We find that the distribution is determined by an intermediate energy scale g with the value between the level spacing in the cavity δ s and the quasiclassical value of the gap E g . 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)] for the distribution of the minigap edge in the opposite limit E Th . 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.

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Section: Introductionsupporting

confidence: 77%

Universal properties of mesoscopic fluctuations of the secondary gap in superconducting proximity systems

et al. 2022

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“…The Chern number fluctuation is related to the Weyl point correlations by simple integrals, and the perturbation theory calculation of the scaling can be modified to include the Wigner surmise for the appropriate ensemble. An example of this has been done in [19], where random matrices obeying the Bogoliubov-de-Gunnes mirror symmetry were considered to describe Weyl points in multichannel Josephson junctions. The band-touching points of different ensembles may have a different co-dimension and are associated with different topological invariant such as the second Chern number.…”

Section: Discussionmentioning

confidence: 99%

“…Later works have shown the correlations of the degeneracy points to exhibit perfect screening [17] and analyzed the correlations of the Berry curvature [18]. A modified version of this model comprised of random matrices obeying the Bogoliubov-de-Gunnes mirror symmetry was also considered to describe the Weyl points in multichannel josephson junctions [19].…”

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confidence: 99%

Fluctuation of Chern Numbers in a Parametric Random Matrix Model

Lin¹,

Kuo²,

Arovas³

et al. 2022

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Band-touching Weyl points in Weyl semimetals give rise to many novel characteristics, one of which the presence of surface Fermi-arc states that is topologically protected. The number of such states can be computed by the Chern numbers at different momentum slices, which fluctuates with changing momentum and depends on the distribution of Weyl points in the Brillouin zone. For realistic systems, it may be difficult to locate the momenta at which these Weyl points and Fermi-arc states appear. Therefore, we extend the analysis of a parametric random matrix model proposed by Walker and Wilkinson to find the statistics of their distributions. Our numerical data shows that Weyl points with opposite polarities are short range correlated, and the Chern number fluctuation only grows linearly for a limited momentum difference before it saturates. We also find that the saturation value scales with the total number of bands. We then compute the short-range correlation length from perturbation theory, and derive the dependence of the Chern number fluctuation on the momentum difference, showing that the saturation results from the short-range correlation.

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Abundance of Weyl points in semiclassical multi-terminal superconducting nanostructures

Cited by 2 publications

References 44 publications

Universal properties of mesoscopic fluctuations of the secondary gap in superconducting proximity systems

Universal properties of mesoscopic fluctuations of the secondary gap in superconducting proximity systems

Fluctuation of Chern Numbers in a Parametric Random Matrix Model

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