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

T. L. Einstein
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Abstract

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 $β(β-2)/4$. 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}: $p_β(0,s) \approx a s^β\exp(-b s^2)$. The value of $β$ is taken to best fit the data; typically $2 \le β\le 10$. 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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BibTeXRIS

T. L. Einstein. 2003-06-12. Applications of Ideas from Random Matrix Theory to Step Distributions on "Misoriented" Surfaces. https://doi.org/10.1007/s00023-003-0964-4

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