Spatial Ordering of Defects and Conductivity of Functionalized Graphene

Recently, it was predicted that an RKKY-type interaction between adatoms in graphene can drive an ordering transition to a state with broken sublattice symmetry (arXiv:1004.3678). In this state, due to Bragg scattering of electron waves on the sublattice modulation, a gap opens up at the Dirac point (DP). Here we investigate the effect of ordering on the transport properties, finding that upon transition from disordered state to an ordered state the conductivity is increased (reduced) at energies away (near) DP. This behavior can be understood as a result of coherent Bragg scattering in the ordered state. The conductivity change can serve as a direct signature of adatom ordering.