Origins of charge density wave in novel Pt-based superconductors: SrPt$_{2}$As$_{2}$ and LaPt$_{2}$Si$_{2}$

The intriguing coexistence of the charge density wave (CDW) and superconductivity in SrPt$_{2}$As$_{2}$ and LaPt$_{2}$Si$_{2}$ has been investigated by using the ab initio density functional theory band structure and phonon calculations. We have found that the local split distortions in the [As-Pt-As] layers play an essential role in driving the five-fold supercell CDW instability as well as the phonon softening instability in SrPt$_{2}$As$_{2}$. In contrast to SrPt$_{2}$As$_{2}$, the CDW and phonon softening instabilities in LaPt$_{2}$Si$_{2}$ occur without split positions of Pt, indicating that the driving mechanisms of the CDW in SrPt$_{2}$As$_{2}$ and LaPt$_{2}$Si$_{2}$ are different. The phonon calculations, however, suggest that the CDW and the superconductivity coexist in [X-Pt-X] layers (X = As or Si) in both cases.