Roughening of Reconstructed Crystal Surfaces and the Hubbard Model

TL;DR

This paper models reconstructed crystal surfaces using a Hubbard model analogy, predicting a new rough phase with incommensurate correlations and complex phase transitions, expanding understanding of surface roughening phenomena.

Contribution

It introduces a novel phase diagram for reconstructed surfaces, revealing incommensurate rough phases and detailed transition types based on the Hubbard model mapping.

Findings

Discovery of a new rough phase with incommensurate correlations.

Identification of phase transition types including KT and Ising transitions.

Prediction of complex phase structure depending on the reconstruction parameter p.

Abstract

We consider a model of a reconstructed crystal surface, first considered by Villain and Vilfan (Europhys. Lett. 12, p. 523 (1990) and Surf. Sci. 257, p. 368 (1991)) for the gold (110) surface, in which roughening occurs via the formation of anisotropic steps traversing the entire length of the crystal. The model is studied by a mapping to a spin--1/2 Fermion system in 1+1 dimensions, which, in the absence of islands, is precisely the Hubbard model. We consider a general $\pbyo$ reconstruction, in the presence of inter--step interactions and closed islands. Our analysis predicts the existence of a new type of rough phase, with incommensurate correlations in the reconstruction order parameter and unusual momentum space singularities at a characteristic ``Fermi momentum'' and its harmonics, analagous to the Luttinger liquid of one--dimensional Fermions. The general phase structure for $p>1$ is as follows: for $p>2$, there is a flat ordered (FO), a rough incommensurate (RI), and a flat incommensurate phase (FI). The FO--RI and FO--FI transitions are of the commensurate to incommensurate type, and the FI--RI transition is in the Kosterlitz--Thouless (KT) universality class. For $p=2$, the FI phase is replaced by a flat disordered phase (FD), and there may be a new rough disordered phase (RD). The FO--FD transition is now of Ising type, and the FD--RD and RI--RD transitions are in the KT universality class.