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

TL;DR

This paper investigates the formation of step bunches on vicinal surfaces due to competing interactions, revealing phase transitions and quantum n-mers, with implications for understanding surface morphology and experimental observations.

Contribution

It introduces a model combining short-range attraction and long-range repulsion to explain step bunching and connects classical surface phenomena to quantum n-mers via a bosonic system mapping.

Findings

Identification of phase transitions with varying temperature and interaction ratios.

Large step bunches correspond to known groove structures at zero temperature.

Proposal of experimental observations of bunch phases on Si surfaces.

Abstract

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 $n_b$ 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.