Substrate effect on the band gap of semiconducting atomic wires

The electronic structure of free-standing and supported semiconducting atomic wires is investigated using a combination of first-principles density functional theory (DFT) and many-body perturbation theory (MBPT). The band gaps predicted from DFT for SiH$_{\mathrm{2}}$ and GeH$_{\mathrm{2}}$ atomic wires are unaffected by the presence of the substrate, whereas the gaps calculated using MBPT under the \textit{GW} approximation are reduced by about 1eV when the wires are supported. The reduction in the band gap is attributed to a change in the electronic correlation energy, which can be understood as a screened Coulomb interaction. These results highlight the importance of the role played by the substrate in manipulating the electronic and optical properties of quantum confined Si and Ge systems.