Quantum cascade of new correlated phases in trigonally warped bilayer graphene

Divergent density of states offers the unique opportunity to explore a wide variety of correlated electron physics. In the thinnest limit, this has been predicted and verified in the ultra-flat 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-driven phases at charge neutrality, such as layer antiferromagnet and quantum anomalous Hall octet. Here we report the discovery of a cascade of novel correlated phases in the vicinity of electric-field-controlled Lifshitz transitions and van Hove singularities in trigonally warped bilayer graphene. We provide compelling evidence for the observation of Stoner ferromagnets - half and quarter metals. More prominently, we identify signatures consistent with a topologically nontrivial Wigner-Hall crystal at zero magnetic field and its transition to a trivial Wigner crystal, as well as two correlated metals whose behavior deviates from standard Fermi liquids. Our results in this reproducible, tunable, simple system opens a new chapter for studying strongly correlated electrons.