Probing the order parameter symmetry of two-dimensional superconductors by twisted Josephson interferometry

Probing the superconducting order parameter symmetry is a crucial step towards understanding the pairing mechanism in unconventional superconductors. Inspired by the recent discoveries of superconductivity in various van der Waals materials, and the availability of the relative twist angle as a continuous tuning knob in these systems, we propose a general setup for probing the order parameter symmetry of two-dimensional superconductors in twisted Josephson junctions. The junction is composed of an anisotropic s-wave superconductor as a probe and another superconductor with an unknown order parameter symmetry. Assuming momentum-resolved tunneling, we investigate signatures of different order parameter symmetries in the twist angle dependence of the critical current, the current-phase relations, and magnetic field dependence. As a concrete example, we study a twisted Josephson junction between NbSe2 and magic angle twisted bilayer graphene.Comment: 15 pages, 5 figure

Intervalley coherence and intrinsic spin-orbit coupling in rhombohedral trilayer graphene

Rhombohedral graphene multilayers provide a clean and highly reproducible platform to explore the emergence of superconductivity and magnetism in a strongly interacting electron system. Here, we use electronic compressibility and local magnetometry to explore the phase diagram of this material class in unprecedented detail. We focus on rhombohedral trilayer in the quarter metal regime, where the electronic ground state is characterized by the occupation of a single spin and valley isospin flavor. Our measurements reveal a subtle competition between valley imbalanced (VI) orbital ferromagnets and intervalley coherent (IVC) states in which electron wave functions in the two momentum space valleys develop a macroscopically coherent relative phase. Contrasting the in-plane spin susceptibility of the IVC and VI phases reveals the influence of graphene's intrinsic spin-orbit coupling, which drives the emergence of a distinct correlated phase with hybrid VI and IVC character. Spin-orbit also suppresses the in-plane magnetic susceptibility of the VI phase, which allows us to extract the spin-orbit coupling strength of $\lambda \approx 50\mu$eV for our hexagonal boron nitride-encapsulated graphene system. We discuss the implications of finite spin-orbit coupling on the spin-triplet superconductors observed in both rhombohedral and twisted graphene multilayers