Anderson transition in a multiply-twisted helix

We investigated the Anderson transition in a multiply-twisted helix in which a helical chain of components, i.e., atoms or nanoclusters, is twisted to produce a doubly-twisted helix, which itself can be twisted to produce a triply-twisted helix, and so on, in which there are couplings between adjacent rounds of helices. As the strength of the on-site random potentials increases, an Anderson transition occurs, suggesting that the number of dimensions is 3 for electrons running along the multiply-twisted helix when the couplings between adjacent rounds are strong enough. If the couplings are weakened, the dimensionality becomes less, resulting in localization of electrons. The effect of random connections between adjacent rounds of helices and random magnetic fields that thread the structure is analyzed using the spectral statistics of a quantum particle.