Zhiyu Dong

Rhombohedral graphene multilayers host various broken-symmetry metallic phases as well as superconductors whose pairing mechanism and order parameter symmetry remain unsettled. Strikingly, experiments have revealed prominent superconducting regions in rhombohedral bilayer and trilayer graphene devices with proximity-induced Ising spin-orbit coupling. We propose that these superconductors descend from a common spin-canted normal state that spontaneously breaks a U(1) spin symmetry and thus supports soft magnon modes. In particular, we show that these soft modes can mediate pairing through interband scattering events that are symmetry forbidden in the absence of spin-orbit coupling, thus providing a promising explanation for spin-orbit-enabled pairing. Numerous other experimental observations—including nontrivial dependence of superconductivity on the spin-orbit coupling strength, in-plane magnetic fields, and Fermi surface structure—also naturally follow from our scenario.

Quantum oscillations originating from the quantization of electron cyclotron orbits provide sensitive diagnostics of electron bands and interactions. We report on nanoscale imaging of the thermodynamic magnetization oscillations caused by the de Haas–van Alphen effect in moiré graphene. Scanning by means of superconducting quantum interference device (SQUID)–on-tip in Bernal bilayer graphene crystal axis-aligned to hexagonal boron nitride reveals large magnetization oscillations with amplitudes reaching 500 Bohr magneton per electron in weak magnetic fields, unexpectedly low frequencies, and high sensitivity to superlattice filling fraction. The oscillations allow us to reconstruct the complex band structure, revealing narrow moiré bands with multiple overlapping Fermi surfaces separated by unusually small momentum gaps. We identified sets of oscillations that violate the textbook Onsager Fermi surface sum rule, signaling formation of broad-band particle-hole superposition states induced by coherent magnetic breakdown.

We argue that spin- and valley-polarized metallic phases recently observed in graphene bilayers and trilayers support chiral edge modes that allow spin waves to propagate ballistically along system boundaries without backscattering. The chiral edge behavior originates from the interplay between the momentum-space Berry curvature in Dirac bands and the geometric phase of a spin texture in position space. The edge modes are weakly confined to the edge, featuring dispersion that is robust and insensitive to the detailed profile of magnetization at the edge. This unique character of edge modes reduces their overlap with edge disorder and enhances the mode lifetime. The mode propagation direction reverses upon reversing valley polarization, an effect that provides a clear testable signature of geometric interactions in isospin-polarized Dirac bands.