LAUSR

Spin-orbit coupling in graphene is able to induce various topological phases and is also crucial for potential application in graphene-based spintronics. However, graphene itself exhibits extremely weak spin-orbit coupling, and it is rather challenging to enhance the spin-orbit coupling without drastically affecting its fundamental physical property in graphene via external means. In this paper, we show that the charge-compensated $n\text{\ensuremath{-}}p$ codoping approach not only can overcome the main shortcomings arising from single-element adsorption in graphene but can also result in a large Rashba spin-orbit splitting. As an example, we codope heavy adatoms with outer-shell $p$ electrons (e.g., Tl atoms acting as $n$-type dopants) on $p$-type doped graphene (e.g., by substituting carbon atoms with B atoms). We find the following: (1) Electrostatic attraction between $n$- and $p$-type dopants effectively enhances the adsorption and diffusion barrier of metallic adatoms and suppresses the undesirable formation of clustering. (2) Large Rashba spin-orbit splitting ($\ensuremath{\sim}130\phantom{\rule{0.16em}{0ex}}\mathrm{meV}$ for 6.25% B-Tl-codoped graphene) is produced due to the electrostatic interaction. (3) The charge-compensated nature and mutual screening of $n\text{\ensuremath{-}}p$ codopants preserve the Dirac dispersion of charge carriers to some extent.