Roughening of anisotropically reconstructed surfaces and the Hubbard model

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Abstract
We consider a model of reconstructed crystal surfaces originally considered by Villain and Vilfan [Europhys. Lett. 12, 253 (1990); 13, 285 (1990); Surf. Sci. 257, 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 p×1 reconstruction, in the presence of interstep 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. The new phase is analogous to the Luttinger liquid of one-dimensional fermions. The general phase structure is as follows: For p>2, there is a flat ordered, a rough incommensurate, and a flat incommensurate (FI) phase. For p=2, the FI phase is replaced by a flat disordered phase, and there is a rough disordered-incommensurate phase. The universality classes of all the connecting phase transitions are determined.