TY - JOUR

T1 - Dimensional Crossover of the Integer Quantum Hall Plateau Transition and Disordered Topological Pumping

AU - Ippoliti, Matteo

AU - Bhatt, R. N.

N1 - Funding Information:
This work was supported by DOE BES Grant No. DE-SC0002140. We acknowledge useful conversations with Shivaji Sondhi.
Publisher Copyright:
© 2020 American Physical Society.

PY - 2020/2/27

Y1 - 2020/2/27

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevLett.124.086602

DO - 10.1103/PhysRevLett.124.086602

M3 - Article

C2 - 32167341

AN - SCOPUS:85081787688

VL - 124

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 8

M1 - 086602

ER -