Pseudospin order in monolayer, bilayer and double-layer graphene

Graphene is a gapless semiconductor in which conduction and valence band wavefunctions differ only in the phase difference between their projections onto the two sublattices of the material's two-dimensional honeycomb crystal structure. We explain why this circumstance creates openings for broken symmetry states, including antiferromagnetic states in monolayer and bilayer graphene and exciton condensates in double-layer graphene, which are momentum space analogues of the real-space order common in systems with strong local interactions. We discuss some similarities among, and some differences between, these three broken symmetry states.