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. By employing a finite-size scaling approach and Landauer-B\"{u}ttiker formula, we show that the randomization of adatom distribution greatly weakens the intervalley scattering, but plays a negligible role in spin-orbit couplings. Consequently, such a randomization turns graphene from a trivial insulator into a topological state.
@article{arxiv.1204.3276,
title = {Stabilizing topological phases in graphene via random adsorption},
author = {Hua Jiang and Zhenhua Qiao and Haiwen Liu and Junren Shi and Qian Niu},
journal= {arXiv preprint arXiv:1204.3276},
year = {2015}
}