Dimensional crossover of the integer quantum Hall plateau transition and disordered topological pumping

Matteo Ippoliti; R. N. Bhatt

doi:10.1103/physrevlett.124.086602

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arXiv · 1905.13171

Dimensional crossover of the integer quantum Hall plateau transition and disordered topological pumping

Matteo Ippoliti·R. N. Bhatt

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Abstract

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 $C\neq 0$. 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 large but finite aspect ratio, where the average Thouless conductance also shows anomalous scaling.

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Matteo Ippoliti, R. N. Bhatt. 2020-02-27. Dimensional crossover of the integer quantum Hall plateau transition and disordered topological pumping. https://doi.org/10.1103/physrevlett.124.086602

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