The potentially crucial role of quasi-particle interferences for the growth of silicene on graphite

A comprehensive picture of the initial stages of silicene growth on graphite is drawn. Evidence is shown that quasiparticle interferences play a crucial role in the formation of the observed silicene configurations. We propose, on one hand, that the charge modulations caused by those quantum interferences serve as templates and guide the incoming Si atoms to self-assemble to the unique ( $\sqrt{3}\times \sqrt{3}$)R30° honeycomb atomic arrangement. On the other hand, their limited extension limits the growth to about 150 Si atoms under our present deposition conditions. The here proposed electrostatic interaction finally explains the unexpected stability of the observed silicene islands over time and with temperature. Despite the robust guiding nature of those quantum interferences during the early growth phase, we demonstrate that the window of experimental conditions for silicene growth is quite narrow, making it an extremely challenging experimental task. Finally, it is shown that the experimentally observed three-dimensional silicon clusters might very well be the simple result of the end of the silicene growth resulting from the limited extent of the quasi-particle interferences.