Cascade of isospin phase transitions in Bernal-stacked bilayer graphene at zero magnetic field

Emergent phenomena arising from the collective behaviour of electrons is expected when Coulomb interactions dominate over the kinetic energy, and one way to create this situation is to reduce the electronic bandwidth. Bernal-stacked bilayer graphene intrinsically supports saddle points in the band structure that are predicted to host a variety of spontaneous symmetry-broken states 1 – 7 . Here we show that bilayer graphene displays a cascade of symmetry-broken states with spontaneous spin and valley isospin ordering at zero magnetic field. We independently tune the carrier density and electric displacement field to explore the phase space of isospin order. Itinerant ferromagnetic states emerge near the conduction and valence band edges with complete spin and valley polarization. At larger hole densities, twofold degenerate quantum oscillations manifest in an additional symmetry-broken state that is enhanced by the application of an in-plane magnetic field. Both symmetry-broken states display enhanced layer polarization, suggesting a coupling to the layer degree of freedom 1 , 7 . These states occur in the absence of a moiré superlattice and are intrinsic to natural graphene bilayers. Therefore, we demonstrate that bilayer graphene represents a related but distinct approach to produce collective behaviour from flat dispersion, complementary to engineered moiré structures.