Ballistic Josephson junctions in edge-contacted graphene

Abstract: Hybrid graphene-superconductor devices have attracted much attention since the early days of graphene research. So far, these studies have been limited to the case of diffusive transport through graphene with poorly defined and modest quality graphene-superconductor interfaces, usually combined with small critical magnetic fields of the superconducting electrodes. Here we report graphene based Josephson junctions with one-dimensional edge contacts of Molybdenum Rhenium. The contacts exhibit a well defined, transparent interface to the graphene, have a critical magnetic field of 8 Tesla at 4 Kelvin and the graphene has a high quality due to its encapsulation in hexagonal boron nitride. This allows us to study and exploit graphene Josephson junctions in a new regime, characterized by ballistic transport. We find that the critical current oscillates with the carrier density due to phase coherent interference of the electrons and holes that carry the supercurrent caused by the formation of a Fabry-P\'{e}rot cavity. Furthermore, relatively large supercurrents are observed over unprecedented long distances of up to 1.5 $\mu$m. Finally, in the quantum Hall regime we observe broken symmetry states while the contacts remain superconducting. These achievements open up new avenues to exploit the Dirac nature of graphene in interaction with the superconducting state.

• The paper demonstrates that optimized hBN encapsulated graphene with MoRe edge contacts supports robust ballistic Josephson junction behavior over lengths up to 1.5 µm.
• The paper reports clear Fabry-Pérot oscillations in the critical current as a function of gate voltage, confirming phase-coherent electron transport.
• The paper identifies non-conventional magnetic interference patterns that exceed one flux quantum, suggesting novel quantum interactions in 2D superconducting devices.

Insights into Ballistic Josephson Junctions in Edge-Contacted Graphene

This paper presents a detailed examination of graphene-based Josephson junctions (JJs) with edge contacts utilizing Molybdenum Rhenium (MoRe), encapsulated in hexagonal boron nitride (hBN). The research exploits the transparent and well-defined nature of the graphene-superconductor interfaces alongside the superior electronic quality of graphene, aiming to elucidate phenomena associated with ballistic transport in such systems.

The study notably departs from the conventional diffusive transport paradigm observed in prior graphene-superconductor hybrids, instead ushering in an exploration of ballistic transport scenarios within two-dimensional (2D) structures. By implementing one-dimensional edge contacts, the researchers mitigate issues with interface definition and transparency, which have historically plagued top-contact methodologies, facilitating more reliable Andreev reflections at the superconducting interface.

Key Findings and Methodologies:

• High-Quality Graphene Devices: The encapsulation strategy in hBN allows the research team to achieve exceptionally high-quality graphene, further bolstered by the MoRe contacts which exhibit a critical magnetic field of around 8 T at 4 K. Surprisingly large supercurrents are supported over lengths extending to 1.5 µm, marking a stark enhancement in transport distance compared to prior studies.
• Ballistic Transport Evidence: The research reports clear oscillations in critical current as a function of gate voltage, reminiscent of Fabry-Pérot interference patterns. This behavior underscores the presence of phase-coherent, ballistic electron transport across the junction. Simulation results complement the experimental data, confirming the occurrence of such interference.
• Critical Current Modulation: The paper describes how the critical current modulation corroborates with the normal state conductance oscillations, reinforcing the assertion of coherent ballistic conduction. The phase difference across the junction is methodically mapped with the applied magnetic field, attributing specific resonant behavior to Fabry-Pérot cavity formation.
• New Magnetic Interference Patterns: A deviation from the standard Fraunhofer diffraction pattern, usually observed in JJs, is reported. The magnetic interference pattern periodicity exceeds one flux quantum, suggesting non-conventional quantum mechanical interactions attributable to the equal dimension JJ geometry and ballistic nature of transport.

Implications and Future Directions

The advancements articulated in this study pave the way for deeper investigations into the quantum mechanical behaviors emerging from graphene-superconductor interfaces. The ability to maintain superconductivity in graphene devices over extended distances while retaining ballistic properties invites potential applications in quantum computing and low-dimensional quantum electronics. Moreover, this setup could function as a platform to explore speculative phenomena such as specular Andreev reflection and its implications for quantum Hall measurements.

Furthermore, the distinct transport properties observed could inform improvements in the design of JJ-based qubits and other quantum circuit elements, where edge contact designs could offer superior coherence and integration. As experimental techniques and materials processing continue to advance, the elucidation of novel quantum phases in graphene devices becomes more plausible, potentially expanding the functional landscape of nanoscale technologies. Future work may extend this framework to bilayer graphene systems or other two-dimensional materials, further testing the limits of phase coherence and ballistic transport in increasingly complex quantum systems.