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Avoiding critical-point phonon instabilities in two-dimensional materials: The origin of the stripe formation in epitaxial silicene
The origin of the large-scale stripe pattern of epitaxial silicene on the ZrB$_2$(0001) surface observed by scanning tunneling microscope experiments is revealed by first-principles calculations. Without stripes, the ($\sqrt{3}\times\sqrt{3}$)-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 …