Unification of the Fermion Approach and the Capillary Wave Approach to the Vicinal Surface by the Bosonization

Abstract

The vicinal surface is well described by the terrace-step-kink model below the faceting temperature. On the basis of this model, the statistical-mechanics of the surface is transformed to the one-dimensional free-fermion system. On the other hand, rough surfaces including the vicinal surface are also expressed by the capillary-wave model. The two pictures of the vicinal surface are quite different, but we successfully derive the capillary wave description with the ''correct stiffness tensor'' from the free-fermion description by the bosonization technique. We show that the low-energy fluctuation of the terrace-step-kink model can be expressed by the capillary-wave picture in the sense inclusive of the anisotropic properties.