  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.
