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

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 $C\ne 0$. 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.

arXiv comment5 pages, 3 figures main text + 5 pages, 5 figures supplement. v2: substantially expanded supplemental material, updated figure 3, corrected minor errors. v3: added references

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Cited by in corpus (10)

• Thouless pumping and topology
• Competition and interplay between topology and quasi-periodic disorder in Thouless pumping of ultracold atoms
• Topological photonics: fundamental concepts, recent developments, and future directions
• Effect of disorder on topological charge pumping in the Rice-Mele model
• Splitting of topological charge pumping in an interacting two-component fermionic Rice-Mele Hubbard model
• Interaction Induced Topological Charge Pump
• Interplay between disorder and topology in Thouless pumping on a superconducting quantum processor
• The integer quantum Hall transition: an $S$-matrix approach to random networks
• Absence of disordered Thouless pumps at finite frequency
• Universal localization-delocalization transition in chiral-symmetric Floquet drives