Step-bunching transitions on vicinal surfaces with attractive step interactions

We study vicinal crystal surfaces within the terrace–step–kink model on a discrete lattice. Including both a short-ranged attractive interaction and a long-ranged repulsive interaction arising from elastic forces, we discover a series of phases in which steps coalesce into bunches of nb steps each. The value of nb varies with temperature and the ratio of short- to long-range interaction strengths. For bunches with large number of steps, we show that, at T=0, our bunch phases correspond to the well-known periodic groove structure first predicted by Marchenko. An extension to T>0 is developed. We propose that the bunch phases have been observed in very recent experiments on Si surfaces, and we advance a conjecture explaining the exponent β≈0.5 describing the shape of the observed phase transition curves. Further experiments are suggested. Within the context of a mapping of the model to a system of bosons on a 1D lattice, the bunch phases appear as quantum n-mers.