Broken translational symmetry in an emergent paramagnetic phase of graphene

We show that the spin-density wave state on the partially filled honeycomb and triangular lattices is preempted by a paramagnetic phase that breaks an emergent Z ₄ symmetry of the system associated with the four inequivalent arrangements of spins in the quadrupled unit cell. Unlike other emergent paramagnetic phases in itinerant and localized-spin systems, this state preserves the C ₆ rotational symmetry of the lattice, but breaks its translational symmetry, giving rise to a superlattice structure that can be detected by scanning tunneling microscopy. This emergent phase also has distinctive signatures in the magnetic spectrum that can be probed experimentally.