Applications of Ideas from Random Matrix Theory to Step Distributions on "Misoriented" Surfaces

Details Applications of Ideas from Random Matrix Theory to Step Distributions on "Misoriented" Surfaces Applications of Ideas from Random Matrix Theory to Step Distributions on "Misoriented" Surfaces

2003-06-12

arxiv.org/abs/cond-mat/0306347v1

Ann. Henri Poincare' 4, Suppl. 2, S811-S824 (2003)

Physics

Condensed Matter

Statistical Mechanics

7 pages, 2 figures; based on talk presented at TH-2002, UNESCO, Paris, July 2002; to be published in Ann. Henri Poincare'

Scientific paper

10.1007/s00023-003-0964-4

Arising as a fluctuation phenomenon, the equilibrium distribution of meandering steps with mean separation $<\ell>$ 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 $s< \ell>$ between neighboring steps (analogous to the normalized spacings of energy levels) is well described by a {\it "generalized" Wigner surmise}: $p_{\beta}(0,s) \approx a s^{\beta}\exp(-b s^2)$. The value of $\beta$ is taken to best fit the data; typically $2 \le \beta \le 10$. 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. (conference abstract)

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