Applications of ideas from random matrix theory to step distributions on misoriented surfaces

Arising as a fluctuation phenomenon, the equilibrium distribution of meandering steps with mean separation on a tilted surface can be fruitfully analyzed using results from RMT. The set of step configurations in 2D can be mapped onto the world lines of spinless fermions in 1+1D using the Calogero-Sutherland model. The strength of the (instantaneous, inverse-square) elastic repulsion between steps, in dimensionless form, is beta(beta-2)/4. The distribution of spacings s between neighboring steps (analogous to the normalized spacings of energy levels) is well described by a generalized Wigner surmise: p(beta)(0, s) approximate to as(beta) exp(-bs(2)). The value of beta is taken to best fit the data; typically 2less than or equal tobetaless than or equal to10. The procedure is superior to conventional Gaussian and mean-field approaches, and progress is being made on formal justification. Furthermore, the theoretically simpler step-step distribution function can be measured and analyzed based on exact results. Formal results and applications to experiments on. metals and semiconductors are summarized, along with open questions.