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

Bernal bilayer graphene has long been predicted to host interaction-driven symmetry-breaking states arising from large densities of states near the band edges. While subtle evidence of gapped symmetry-breaking states have been demonstrated at charge neutrality in suspended samples and exchange-driven symmetry breaking often manifests in large magnetic fields, no gapless spin or valley polarized states have been reported within the low-energy flat bands of the system in the absence of a magnetic field. Here, we show that ultra-clean bilayer graphene in fact hosts a series of isospin magnetic phase transitions for both signs of carriers at zero magnetic field. The phase boundaries and degeneracy of each isospin ordered state are further tunable by an external electric displacement field, replacing the role of magnetic field in the analogous quantum Hall ferromagnet. Quantum oscillations of the symmetry-broken states reveal discrete transitions in the degeneracy of each zero-field state and parallel field measurements hint at the underlying isospin order.