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Anderson Localization in the Fractional Quantum Hall Effect.
Songyang Pu1,2, G J Sreejith3, J K Jain1
1Department of Physics, 104 Davey Lab, Pennsylvania State University, University Park, Pennsylvania 16802, USA.
Physical Review Letters
|April 1, 2022
Summary
Localization in fractional quantum Hall states shows a quantitative link to electron localization in Landau levels. This suggests extended states and critical energy behavior, similar to Anderson localization.
Area of Science:
- Condensed Matter Physics
- Quantum Hall Effect
Background:
- The interplay between interactions and disorder is crucial for understanding localization phenomena.
- Fractional quantum Hall states exhibit complex physics due to strong interactions and disorder effects.
Purpose of the Study:
- To investigate the localization physics in fractional quantum Hall states.
- To establish a theoretical correspondence between quasiparticle localization and electron localization.
Main Methods:
- Theoretical analysis of localization in fractional quantum Hall states.
- Mean-field approximation to extend results to finite quasiparticle densities.
Main Results:
- Demonstrated a quantitative correspondence between fractional quantum Hall quasiparticle localization and electron localization in Landau levels.
- Predicted the existence of extended states at a critical energy in the fractional quantum Hall regime.
- Characterized the divergence of localization length near the critical energy.
Conclusions:
- The findings offer compelling theoretical evidence for Anderson localization-like phenomena in fractional quantum Hall states.
- The study predicts observable experimental signatures for localization in these systems.
- The mean-field approach provides a framework for understanding localization with finite quasiparticle densities.
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