Ab initio study of the electronic properties and thermodynamic stability of supported and functionalized two-dimensional Sn films

Using density-functional theory (DFT), we study the growth of pristine and functionalized tin monolayers (Sn-MLs) on three different substrates, CdTe, InSb, and Si(111), and the impact these substrates have on the topological insulating properties of the electronic band structure. The presence of the substrate leads to strain and electronic charge transfer, which cause significant changes in the stability and electronic properties of the supported Sn-ML. Growth of pristine Sn-MLs on Si(111) leads to metallic behavior resembling that of the high-buckled Sn-ML phase; pristine Sn-MLs grown on InSb do not maintain a gap throughout the entire Brillouin zone; and pristine Sn-MLs grown on CdTe are unlikely to exhibit an experimentally observable gap. Provided the charge transfer from the substrate can be compensated, halogen-functionalized Sn-MLs grown on CdTe and InSb are topological insulators, albeit with a reduced band gap compared to their free-standing counterparts (from 0.34 eV for Sn-ML-I to 0.17 eV for InSb-Sn-ML-I). We employ ab initio thermodynamics calculations to study the thermodynamic stability of the halogenated InSb-Sn-MLs and CdTe-Sn-MLs surfaces for a temperature range of 100--1000 K under two extreme environments: ultrahigh vacuum (used in most of the laboratory characterization techniques) and rich-halogen conditions (10% vol. halogen environment). Our results indicate that it is possible to obtain stable topologically insulating Sn-MLs grown epitaxially on lattice-matched substrates.