It is shown, using density functional theory, that a 2D electron gas induced in a monolayer of Pb or Tl adatoms on the $\mathrm{Si}\left(111\right)-1\times 1$ surface is insensitive to the structural asymmetry of the system and its spin polarization is governed by the interaction between the adlayer and the substrate. It is demonstrated that this interaction changes the in-plane inversion symmetry of the charge distribution within the monolayer and can either suppress $\text{[Pb/Si(111)]}$ or enhance $\left[\text{Tl/Si(111)}\right]$ the adatom intra-atomic spin-orbit effect on a Rashba-Bychkov-type spin splitting.

• Received 4 February 2016
• Revised 14 April 2016

DOI:https://doi.org/10.1103/PhysRevB.93.195318