  Bilayer graphene and its thicker cousins with Rhombohedral stacking have
attracted considerable attention because of their susceptibility to a variety
of broken chiral symmetry states. Due to large density-of-states and quantized
Berry phases near their gapless band touching points, each spin-valley flavor
spontaneously transfers charge between layers to yield opening of energy gaps
in quasiparticle spectra and spreading of momentum-space Berry curvatures. In
this article we review the development of theories that predicted such chiral
symmetry breaking and classified the possible topological many-body ground
states, and the observations in recent experiments that are in reasonable
agreement with these theories.
