Fluctuation of a Single Step on the Vicinal Surface-Universal and Non-Universal Behaviors

Abstract

Mean-square fluctuation width of a single step on the vicinal surface, denoted by Δ²(y) (y: distance along the step), is calculated based on the terrace-step-kink picture. For systems with only short-range step-step interactions, both the free-fermion approach and the capillary-wave approach are taken to derive the universal asymptotic behavior Δ²(y)-- A, log, y with A=(π ρ )^-2, where ρ is the step density. We present a general relation between Δ²(y) and the surface height-height correlation function, which connects the universal behavior to the universal Gaussian curvature jump at the facet edge. For the case with long-range (inverse-square) step-step interactions, we combine the exact solution of the Sutherland model with the capillary-wave theory. We successfully derive the non-universal amplitude A=A(ρ, , g) as a function of the coupling constant g.