Spontaneous chiral symmetry breaking in bilayer graphene

•Bilayer graphene is susceptible to a variety of broken chiral symmetry states.•Interactions yield opening of energy gap and spreading of Berry curvature.•We review the theories that predicted/classified the topological ground states.•We discuss the experimental observations that are in agreement with the theories.

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.

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