Secondary “smile”-gap in the density of states of a diffusive Josephson junction for a wide range of contact types

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The superconducting proximity effect leads to strong modifications of the local density of states in diffusive or chaotic cavity Josephson junctions, which displays a phase-dependent energy gap around the Fermi energy. The so-called minigap of the order of the Thouless energy ETh is related to the inverse dwell time in the diffusive region in the limit ETh≪Δ, where Δ is the superconducting energy gap. In the opposite limit of a large Thouless energy ETh≫Δ, a small new feature has recently attracted attention, namely, the appearance of a further secondary gap, which is around two orders of magnitude smaller compared to the usual superconducting gap. It appears in a chaotic cavity just below the superconducting gap edge Δ and vanishes for some value of the phase difference between the superconductors. We extend previous theory restricted to a normal cavity connected to two superconductors through ballistic contacts to a wider range of contact types. We show that the existence of the secondary gap is not limited to ballistic contacts, but is a more general property of such systems. Furthermore, we derive a criterion which directly relates the existence of a secondary gap to the presence of small transmission eigenvalues of the contacts. For generic continuous distributions of transmission eigenvalues of the contacts, no secondary gap exists, although we observe a singular behavior of the density of states at Δ. Finally, we provide a simple one-dimensional scattering model which is able to explain the characteristic “smile” shape of the secondary gap.

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ISO 690REUTLINGER, Johannes, Leonid I. GLAZMAN, Yu V. NAZAROV, Wolfgang BELZIG, 2014. Secondary “smile”-gap in the density of states of a diffusive Josephson junction for a wide range of contact types. In: Physical Review B. 2014, 90(1), 014521. ISSN 0163-1829. eISSN 1095-3795. Available under: doi: 10.1103/PhysRevB.90.014521
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@article{Reutlinger2014Secon-29743,
  year={2014},
  doi={10.1103/PhysRevB.90.014521},
  title={Secondary “smile”-gap in the density of states of a diffusive Josephson junction for a wide range of contact types},
  number={1},
  volume={90},
  issn={0163-1829},
  journal={Physical Review B},
  author={Reutlinger, Johannes and Glazman, Leonid I. and Nazarov, Yu V. and Belzig, Wolfgang},
  note={Article Number: 014521}
}
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