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.

Anomalous Fraunhofer interference in epitaxial superconductor-semiconductor Josephson junctions

“…This behavior has been observed in a wide variety of systems [29,30] including 2DEGs with strong SOI [31]. Deviations from this Fraunhofer form can yield information about the local magnetic field profile [32] as well as the supercurrent density in the junction [33,34]. Recently, such interference mapping has been used to probe edge states arising in two-dimensional topological insulators [35,36] and graphene [37].…”

Observation of Electron Coherence and Fabry–Perot Standing Waves at a Graphene Edge

“…Because the critical current I c (B) equals the magnitude of the complex Fourier transform of the real-space supercurrent distribution J(x), the shape of the interference pattern is determined directly by the spatial distribution of supercurrent across the sample. 5,27 To visualize current flow associated with interfering electron waves, we examine the supercurrent modulations in a B field that arise from a Fraunhofer interference. In a conventional Josephson junction with uniform current density, the normalized critical current obeys I c (B)/I c (0) = |sin(πΦ/Φ 0 )/(πΦ/Φ 0 )|.…”

Spatially resolved edge currents and guided-wave electronic states in graphene

“…Here, following the conventional treatment for wide junctions such that L W , where L is the distance between contacts, we ignore the y dependence. The spatial distribution of supercurrent thus dictates the shape of the interference pattern 13,21,23 . The results obtained with this technique show strikingly different behaviour at high and low carrier densities.…”