Vicinal Surfaces and the Calogero-Sutherland Model

TL;DR

This paper models vicinal crystal surfaces as non-crossing steps influenced by Calogero-Sutherland interactions, revealing a faceting transition between homogeneous and clustered states, with exact solutions aligning with experimental data.

Contribution

It uncovers a critical line in the Calogero-Sutherland model governing surface faceting transitions, providing exact expressions for measurable surface properties.

Findings

Identifies a faceting transition driven by step interactions.

Derives exact solutions matching experimental observations.

Describes a critical line in the Calogero-Sutherland model for surface morphology.

Abstract

A miscut (vicinal) crystal surface can be regarded as an array of meandering but non-crossing steps. Interactions between the steps are shown to induce a faceting transition of the surface between a homogeneous Luttinger liquid state and a low-temperature regime consisting of local step clusters in coexistence with ideal facets. This morphological transition is governed by a hitherto neglected critical line of the well-known Calogero-Sutherland model. Its exact solution yields expressions for measurable quantities that compare favorably with recent experiments on Si surfaces.