Hierarchical band clustering and fractal spectra in incommensurate systems
- 1 August 1987
- journal article
- letter
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 20 (11) , L739-L744
- https://doi.org/10.1088/0305-4470/20/11/012
Abstract
An analytic derivation is given of rules exactly describing the hierarchical band clustering in the spectrum of Harper's equation for various incommensurate systems. These rules, involving transformations of the incommensurability parameter phi , are shown to apply exactly for arbitrary coupling strength. The approach also provides energy scale factors and hence the fractal dimension Df(=0.50+or-0.01) of the self-similar spectrum occurring when phi takes a fixed point value phi g (the golden mean).This publication has 13 references indexed in Scilit:
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