Step-Bunching Transitions on Vicinal Surfaces and Quantum n-mers

We study vicinal crystal surfaces within the terrace-step-kink model on a discrete lattice. Includ-ing 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 n b steps each. The value of n b 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 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.