Strong and weak localization in a ballistic quantum chain

Abstract

We study coherent electron transport in a quantum network or superlattice formed by connecting chaotic ballistic quantum dots via barriers of arbitrary transparencies in a chain topology. We show that the emergence of localization effects, both weak and strong, depend on the way the infinite dot scaling limit is taken. In the localized regime, we found evidence of single parameter scaling and deviations from uniformity in the distribution of the unitary matrices in the polar decomposition of the system’s transfer-matrix. In the metallic regime, we show that recent predictions of anomalous properties in a double scaling limit, in which the barriers’ transparencies are changed along with the number of dots, can be interpreted as a two-parameter scaling theory, which cannot be derived from the Dorokhov–Mello–Pereyra–Kumar equation.