Hybridization of topologically distinct quartet modes in three-terminal graphene Josephson junctions

Abstract: Multiterminal Josephson junctions offer a powerful playground for exploring exotic superconducting and topological phenomena beyond the reach of conventional two-terminal devices. In this work, we present the direct spectroscopic observation of Cooper quartet resonances, a signature of correlated tunneling of two Cooper pairs across the device, in a graphene three-terminal Josephson junction (3TJJ). Using tunneling spectroscopy, we visualize how Andreev bound states (ABS) evolve across a two-dimensional superconducting phase space, controlled by the two independent phase differences in the 3TJJ. These measurements reveal sharp local minima in the differential conductance spectra locked in a specific phase condition of superconducting phase variables. The resulting quantized trajectories around the compact torus of the superconducting phase variables reveal an underlying topological winding in the multipair transport. To interpret our results, we develop a theoretical model that connects the observed quartet resonances to the coherent hybridization of multiple ABS branches, a hallmark of the rich pairing process enabled by multiterminal geometries. Our results highlight the potential of multiterminal superconducting devices to host engineered superconducting states and pave the way for new approaches to topological band structure design based on phase-controlled, higher-order superconducting transport.