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arXiv:2607.11721

High-field Josephson effect enabled by a moiré Hofstadter spectrum

A. Díez-Carlón, M. Cárdenes Wuttig, N. Wei, D. Ivanov, P. Altpeter, P. Hakonen, K. Watanabe, T. Taniguchi, L. I. Glazman, D. K. Efetov

cond-mat.mes-hallcond-mat.supr-conquant-phSubmitted Jul 13, 2026• Announced Jul 14, 2026
arXivHTMLPDF

Abstract

Magnetic fields generally suppress phase-coherent Josephson transport, limiting superconducting interferometry to relatively low fields. Here we show that moiré-engineered graphene Josephson junctions can overcome this constraint. Using ballistic graphene/hBN junctions, we establish phase-coherent Andreev transport through Fabry-Pérot oscillations and Fraunhofer interference that persist across both the primary Dirac cone and reconstructed moiré minibands. We then demonstrate phase-coherent Josephson interference up to 6 T in the fractal Hofstadter-butterfly regime, well beyond the range expected for conventional ballistic graphene junctions. Comparison with Hofstadter-spectrum calculations reveals that superconductivity survives where the moiré potential transforms Landau levels with quenched group velocity into dispersive magnetic Bloch bands with finite quasiparticle group velocity, enabling extended electron-hole Andreev trajectories across the junction. Our results show that Hofstadter minibands can stabilize phase-coherent superconductivity deep into the parameter domain conventionally associated with the quantum Hall regime, establishing a new platform for high-field superconducting interferometry.

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Bulletin of the American Physical Society•Mar 17, 2017•0 citations
Magnetic fields generally suppress phase-coherent Josephson transport, limiting superconducting interferometry to relatively low fields. Here we show that moiré-engineered graphene Josephson junctions can overcome this constraint. Using ballistic graphene/hBN junctions, we establish phase-coherent Andreev transport through Fabry-Pérot oscillations and Fraunhofer interference that persist across both the primary Dirac cone and reconstructed moiré minibands. We then demonstrate phase-coherent Josephson interference up to 6 T in the fractal Hofstadter-butterfly regime, well beyond the range expected for conventional ballistic graphene junctions. Comparison with Hofstadter-spectrum calculations reveals that superconductivity survives where the moiré potential transforms Landau levels with quenched group velocity into dispersive magnetic Bloch bands with finite quasiparticle group velocity, enabling extended electron-hole Andreev trajectories across the junction. Our results show that Hofstadter minibands can stabilize phase-coherent superconductivity deep into the parameter domain conventionally associated with the quantum Hall regime, establishing a new platform for high-field superconducting interferometry.
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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.
We study the transition of $\ensuremath{\nu}=1/3$ and 2/52/52/5 fractional quantum Hall states of the honeycomb Hofstadter model as we tune to a two-orbital moir\'e superlattice Hamiltonian, motivated by the flat bands of twisted bilayer graphene in a perpendicular magnetic field. In doing so, we address the extent to which these states survive in moir\'e systems and analyze the nature of the transition. Through the use of a Peierls substitution, we determine the Landau-level splitting for the moir\'e Hamiltonian, and study the structure of the Chern bands for a range of magnetic flux per plaquette. We identify topological flat bands in the spectrum at low energies, with numerically tractable lattice geometries that can support the fractional quantum Hall effect. As we tune the model, we find that the orbital-polarized $\ensuremath{\nu}=1/3$ and 2/52/52/5 states corresponding to the honeycomb Hofstadter model survive up to $\ensuremath{\approx}30%$ of typical moir\'e superlattice parameters, beyond which they transition into an insulating phase. We present evidence for this through density matrix renormalization group calculations on an infinite cylinder, by verifying the charge pumping, spectral flow, entanglement scaling, and conformal field theory edge counting. We conclude that fractional quantum Hall states from the Hofstadter model can persist up to hopping amplitudes of the same order as those typical for moir\'e superlattice Hamiltonians, which implies generally that fractional states for moir\'e superstructures can be discerned simply by analyzing the dominant terms in their effective Hamiltonians.
Controlling the energy spectrum of quantum-coherent superconducting circuits, i.e., the energies of excited states, the circuit anharmonicity, and the states' charge dispersion, is essential for designing performant qubits. This control is usually achieved by adjusting the circuit's geometry. In situ control is traditionally obtained via an external magnetic field, in the case of tunnel Josephson junctions. More recently, semiconductor-weak-links-based Josephson junctions have emerged as an alternative building block with the advantage of tunability via the electric-field effect. Gate-tunable Josephson junctions have been succesfully integrated in superconducting circuits using, for instance, semiconducting nanowires or two-dimensional electron gases. In this Letter we demonstrate, in a graphene superconducting circuit, a large gate tunability of qubit properties: frequency, anharmonicity, and charge dispersion. We rationalize these features using a model considering the transmission of Cooper pairs through Andreev bound states. Noticeably, we show that the high transmission of Cooper pairs in such weak link strongly suppresses the charge dispersion. Our Letter illustrates the potential for graphene-based qubits as versatile building blocks in advanced quantum circuits.
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.
We present measurements of DC superconducting quantum interference devices based on Nb/graphene/Nb Josephson junctions. The superconducting proximity effect in graphene can be used to build Josephson junctions whose critical current can be controlled by field-effect gates. These junctions combine the tunability of semiconductor Josephson junctions with the high critical currents and low contact resistances of metal SNS junctions. By using local gates, the SQUID junction critical currents can be modified individually and this allows the sensitivity and symmetry of the SQUID to be controlled in-situ. We compare the critical current of the SQUID with simulations that include a non-sinusoidal current phase relation in the junctions, as expected for ballistic graphene junctions. We also investigate the transfer function of the device in both symmetric and asymmetric configurations and find a highest transfer function of 300 μV/Φ0. Graphene Josephson junctions have the potential to add functionality to existing technologies; for example, to make SQUID magnetometers with tunable sensitivity or superconducting qubits with fast electrical control.