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The relation between the geometry of a two-dimensional sample and its equilibrium physical properties is exemplified here for a system of noninteracting electrons on a M\"obius strip. Dispersion relation for a clean sample is derived and its persistent current under moderate disorder is elucidated, using statistical analysis pertinent to a single sample experiment. The flux periodicity is found to be distinct from that in a cylindrical sample, and the essential role of disorder in the ability to experimentally identify a M\"obius strip is pointed out.
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Yakubo et al. (2003) studied this question.
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