The origin of the large-scale stripe pattern of epitaxial silicene on the ZrB2(0001) surface observed by scanning tunneling microscopy experiments is revealed by first-principles calculations. Without stripes, the (√3×√3)-reconstructed, one-atom-thick Si layer is found to exhibit a “zero-frequency” phonon instability at the M point. In order to avoid a divergent response, the relevant phonon mode triggers the spontaneous formation of a new phase with a particular stripe pattern offering a way to lower both the atomic surface density and the total energy of silicene on the particular substrate. The observed mechanism is a way for the system to handle epitaxial strain and may therefore be more common in two-dimensional epitaxial materials exhibiting a small lattice mismatch with the substrate.
