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Spontaneous Chiral Symmetry Breaking in Bilayer Graphene

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.