Proximity-induced superconductivity and Josephson critical current in quantum spin Hall systems

Abstract

We consider recent experiments on wide superconductor-quantum spin Hall insulator (QSHI)-superconductor Josephson junctions, which have shown preliminary evidence of proximity-induced superconductivity at the edge-modes of the QSHI system based on an approximate analysis of the observed Fraunhofer spectra of the Josephson critical current as a function of the applied magnetic field. Using a completely independent exact numerical method involving a non-linear constrained numerical optimization, we calculate the supercurrent profiles, comparing our results quantitatively with the experimental Fraunhofer patterns in both HgCdTe and InAs-GaSb based QSHI Josephson junctions. Our results show good qualitative agreement with the experiments, verifying that the current distribution in the 2D sample indeed has peaks at the sample edges when the system is in the QSHI phase, thus supporting the interpretation that superconductivity has indeed been induced in the QSHI edge-modes. On the other hand, our numerical work clearly demonstrates that it will be very difficult, if not impossible, to obtain detailed quantitative information about the super-current distribution just from the analysis of the Josephson Fraunhofer spectra, and, therefore, conclusions regarding the precise width of the edge modes or their topological nature are most likely premature at this stage.

9 pages, 6 figures

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Cited by in corpus (22)

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• Quantum interference of edge supercurrents in a two-dimensional topological insulator
• Anomalous Fraunhofer patterns in gated Josephson junctions based on the bulk-insulating topological insulator BiSbTeSe2
• $h/e$ superconducting quantum interference through trivial edge states in InAs
• Visualization of phase-coherent electron interference in a ballistic graphene Josephson junction
• Even-odd flux quanta effect in the Fraunhofer oscillations of an edge-channel Josephson junction
• Induced spectral gap and pairing correlations from superconducting proximity effect
• Crossed Andreev Reflection in InSb Flake Josephson Junctions
• Quantum interference in topological insulator Josephson junctions
• Giant supercurrent states in a superconductor-InAs/GaSb-superconductor junction
• Gate-defined Josephson weak-links in monolayer $\mathrm{WT}{\mathrm{e}}_2$
• High magnetic field stability in a planar graphene-NbSe${}_2$ SQUID
• Tip-induced Superconductivity
• Effects of spin-orbit coupling and in-plane Zeeman fields on the critical current in two-dimensional hole gas SNS junctions
• Quantum interference in a superconductor-${\mathrm{MnBi}}_2{\mathrm{Te}}_4$-superconductor Josephson junction
• Edge supercurrent in Josephson junctions based on topological materials
• Enhanced zero-bias conductance peak and splitting at mesoscopic interfaces between an $s$-wave superconductor and a 3D Dirac semimetal
• Reconstructing Critical Current Density in Josephson Junctions with Phase Non-linearity
• Local Control of Supercurrent Density in Epitaxial Planar Josephson Junctions