The differences in energy between electronic bands due to valley splitting are of paramount importance in interpreting transport spectroscopy experiments on state-of-the-art quantum devices defined by scanning tunneling microscope lithography. We develop a plane-wave density functional theory description of these systems which is size-limited due to computational tractability. We then develop a less resource-intensive alternative via localized basis functions, retaining the physics of the plane-wave description, and extend this model beyond the capability of plane-wave methods to determine the ab initio valley splitting of well-isolated \delta-layers. In obtaining agreement between plane-wave and delocalized methods, we show that the valley splitting has been overestimated in previous ab initio calculations by more than 50%.
@article{arxiv.1201.3751,
title = {Ab initio calculation of valley splitting in monolayer \delta-doped phosphorus in silicon},
author = {Daniel W. Drumm and Akin Budi and Manolo C. Per and Salvy P. Russo and Lloyd C. L. Hollenberg},
journal= {arXiv preprint arXiv:1201.3751},
year = {2013}
}