Observation of two-stage layering transitions for solidHe4on graphite

We have made measurements of the layer-by-layer growth of solid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ from the superfluid onto a graphite substrate, and at temperatures below 0.95 K and up to eight layers we have observed remarkable and unexpected behavior which gives clear evidence of a two-stage layering transition. It is speculated that the two stages may result from the different binding energies at step and kink sites (possibly involving quantum kinks) or an incommensurate-commensurate transition.