Stabilizing topological phases in graphene via random adsorption

We study the possibility of realizing topological phases in graphene with randomly distributed adsorbates. When graphene is subjected to periodically distributed adatoms, the enhanced spin-orbit couplings can result in various topological phases. However, at certain adatom coverages, the intervalley scattering renders the system a trivial insulator. Using both finite-size scaling method and transport calculation, we show that when the adatom distribution becomes random, the intervalley scattering is weakened, but other quantities (e.g. spin-orbit couplings, and exchange field) are not affected. This finding points out that the topological states are graphene-favored ground states in the presence of randomly distributed adtoms. \\[4pt] Hua Jiang, Zhenhua Qiao, Haiwen Liu, Junren Shi and Qian Niu, Phys. Rev. Lett. \textbf{109}, 116803 (2012).