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 rotational symmetry of the lattice but breaks its translational symmetry, giving rise to a super-lattice 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.
@article{arxiv.1203.5776,
title = {Broken translational symmetry in an emergent paramagnetic phase of graphene},
author = {Gia-Wei Chern and Rafael M. Fernandes and Rahul Nandkishore and Andrey V. Chubukov},
journal= {arXiv preprint arXiv:1203.5776},
year = {2012}
}