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

Area of Science:

• Condensed Matter Physics
• Quantum Hall Effect
• Topological States of Matter

Background:

• The quantum Hall effect exhibits plateau transitions, crucial for understanding topological phases.
• Rectangular tori provide a tunable geometry to study dimensional crossovers in critical phenomena.

Purpose of the Study:

• Investigate the quantum Hall plateau transition on rectangular tori.
• Analyze the impact of varying torus aspect ratio on critical behavior.
• Resolve the apparent paradox of localized states retaining topological properties in the thin-torus limit.

Main Methods:

• Numerical simulations on rectangular tori.
• Mapping the thin-torus quantum Hall system to a disordered Thouless pump.
• Characterizing the crossover between 1D and 2D regimes.

Main Results:

• Observed a drastic change in critical behavior as the torus aspect ratio increases.
• Demonstrated that in the thin-torus limit, all states are Anderson localized, yet many retain a non-zero Chern number.
• Established a quantitative characterization of the 1D-2D dimensional crossover.
• Found anomalous scaling in the average Thouless conductance.

Conclusions:

• The thin-torus quantum Hall system can be mapped to a disordered Thouless pump, explaining the persistence of topological properties in localized states.
• The Chern number in this context corresponds to the winding number in the Thouless pump model.
• The study quantitatively describes the dimensional crossover and associated anomalous scaling in conductance.