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arXiv:2609.24572

The Superconducting Talbot Effect in Phased-Array Josephson Junctions

Hechen Ren, Ziying Li

cond-mat.mes-hallcond-mat.supr-conquant-phSubmitted Sep 21, 2026• Announced Sep 22, 2026
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Abstract

We introduce the superconducting Talbot effect---a macroscopic quantum self-imaging phenomenon occurring when proximitized Cooper pairs propagate through a ballistic two-dimensional electron gas. By configuring periodic superconducting leads into a phased-array Josephson junction with programmable phase differences, we demonstrate active steering of the resulting superconducting Talbot carpet. To overcome transport resolution limits, we design a Vernier-scale collector array that performs sub-wavelength sampling of the fractional Talbot pattern. This approach maps real-space quantum interference with high robustness to disorder, enabling direct extraction of Fermi wavelengths across helical, spin-degenerate, and spin-orbit-split Fermi surfaces. Tight-binding numerical calculations on a square lattice validate the real-space interference patterns. Our results establish a versatile framework for coherent wavefront engineering and quantum materials diagnostics in superconducting optics.

Comments
14 pages, 5 figures

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Spatially resolved control of coherent electron transport offers a route to understanding and engineering interference phenomena in hybrid superconducting devices. Here, we use Scanning Gate Microscopy (SGM) to investigate Fabry-Pérot (FP) interference in the n-p-n cavity of a ballistic graphene Josephson junction. Spatial maps of the superconducting switching current and normal-state conductance reveal circular interference fringes arising from two distinct effects of the SGM tip potential. A global shift of the Fermi wave vector modulates the FP resonances of the cavity, while a local perturbation produces additional oscillations that persist at fixed Fermi wave vector as the tip bias is varied. An analytical model identifies the origin of this local response with coherent electron lensing, in which the tip modifies the phase accumulated along interfering trajectories. The measured fringe patterns in the switching current indicate that this mechanism affects superconducting transport, consistent with tip-induced shifts of the resonance conditions for Andreev bound states. These results establish SGM as a tunable local lens for controlling interference in superconducting ballistic graphene devices.