Intrinsic and Extrinsic Spin-Orbit Coupling in Rhombohedral Graphene, Part I

Rhombohedral graphene multilayers host magnetism and both spin singlet and triplet superconductivity when doped through displacement field tuned van Hove singularities located near the band edge [1-4]. The role of the spin degree of freedom has been a key outstanding question in the many-body physics of these systems. In this first of two talks, we use high resolution capacitance and nanoSQUID on Tip (nSOT) magnetometry to investigate the phase diagram of generalized magnetic phases in rhombohedral graphene. I will focus on the “quarter metal” regime, where a valley imbalanced phase with a finite orbital magnetic moment competes with an intervalley coherent phase in which electron wave functions in the two momentum space valleys develop a macroscopically coherent relative phase. Unexpectedly, the delicate balance between these nearly degenerate phases reveals the influence of intrinsic spin-orbit coupling, which we measure to have a strength of approximately 50 micro-eV. In the intervalley coherent regime, spin orbit coupling nucleates new ground states with in- and out-of-plane spin anisotropy, with implications for the phase diagram of spin-triplet superconductivity observed in both bi- and trilayer graphene.



[1] Zhou, H., Xie, T., Ghazaryan, A., et al. Nature 598, 429–433 (2021).

[2] Zhou, H., Xie, T., Taniguchi, T. et al. Nature 598, 434–438 (2021).

[3] Zhou, H., Holleis, L., Saito, Y. et al. Science 375, 774-778 (2022).

[4] Zhang, Y., Polski, R., Thomson, A. et al. Nature 613, 268–273 (2023).