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

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

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REUTLINGER, Johannes, Leonid 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. 90(1), 014521. ISSN 0163-1829. eISSN 1095-3795. Available under: doi: 10.1103/PhysRevB.90.014521

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

Nazarov, Yu V. 2014 2015-02-04T08:55:26Z Secondary “smile”-gap in the density of states of a diffusive Josephson junction for a wide range of contact types 2015-02-04T08:55:26Z Reutlinger, Johannes Reutlinger, Johannes Belzig, Wolfgang eng 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 E<sub>Th</sub> is related to the inverse dwell time in the diffusive region in the limit E<sub>Th</sub>≪Δ, where Δ is the superconducting energy gap. In the opposite limit of a large Thouless energy E<sub>Th</sub>≫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. Belzig, Wolfgang Glazman, Leonid Glazman, Leonid Nazarov, Yu V.

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