Dimensional Crossover of the Integer Quantum Hall Plateau Transition and Disordered Topological Pumping

• Published in: Physical review letters Vol. 124; no. 8; p. 086602
• Main Authors: Ippoliti, Matteo, Bhatt, R N
• Format: Journal Article
• Language: English
• Published: United States 27.02.2020
• ISSN: 1079-7114
• DOI: 10.1103/physrevlett.124.086602

We study the quantum Hall plateau transition on rectangular tori. As the aspect ratio of the torus is increased, the two-dimensional critical behavior, characterized by a subthermodynamic number of topological states in a vanishing energy window around a critical energy, changes drastically. In the thin-torus limit, the entire spectrum is Anderson localized; however, an extensive number of states retain a Chern number C≠0. We resolve this apparent paradox by mapping the thin-torus quantum Hall system onto a disordered Thouless pump, where the Chern number corresponds to the winding number of an electron's path in real space during a pump cycle. We then characterize quantitatively the crossover between the one- and two-dimensional regimes for finite torus thickness, where the average Thouless conductance also shows anomalous scaling.