Localization in a one-dimensional Thue-Morse chain

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Abstract
The mean resistance of a one-dimensional wire is calculated with the use of Landauer formula for three types of arrangements: the random, Thue-Morse, and Fibonacci chain for which the positions of the atoms and the scattering strengths are modulated according to the prescribed rules. Comparison of the obtained numerical results shows that for the position modulation, a Thue-Morse chain is more localized than a Fibonacci chain, while for the scattering strength modulation it is less localized. It is shown that the Thue-Morse chain can be switched from being localized to being extended when the ratio of the strength modulation to the position modulation is increased. A similar change occurs in the generalized Thue-Morse chain.