Quantum cascade of correlated phases in trigonally warped bilayer graphene.

Divergent density of states offers an opportunity to explore a wide variety of correlated electron physics. In the thinnest limit, this has been predicted and verified in the ultraflat bands of magic-angle twisted bilayer graphene, the band touching points of few-layer rhombohedral graphite and the lightly doped rhombohedral trilayer graphene. The simpler and seemingly better understood Bernal bilayer graphene is also susceptible to orbital magnetism at charge neutrality leading to layer antiferromagnetic states or quantum anomalous Hall states. Here we report the observation of a cascade of correlated phases in the vicinity of electric-field-controlled Lifshitz transitions and van Hove singularities in Bernal bilayer graphene. We provide evidence for the observation of Stoner ferromagnets in the form of half and quarter metals. Furthermore, we identify signatures consistent with a topologically non-trivial Wigner-Hall crystal at zero magnetic field and its transition to a trivial Wigner crystal, as well as two correlated metals whose behaviour deviates from that of standard Fermi liquids. Our results in this reproducible, tunable, simple system open up new horizons for studying strongly correlated electrons.