Universality of quantum phase transitions in the integer and fractional quantum Hall regimes

Simrandeep Kaur, Tanima Chanda, Kazi Rafsanjani Amin, Divya Sahani, Kenji Watanabe, Takashi Taniguchi, Unmesh Ghorai, Yuval Gefen, G. J. Sreejith and Aveek Bid ()
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Simrandeep Kaur: Indian Institute of Science
Tanima Chanda: Indian Institute of Science
Kazi Rafsanjani Amin: Chalmers University of Technology
Divya Sahani: Indian Institute of Science
Kenji Watanabe: National Institute for Materials Science
Takashi Taniguchi: National Institute for Materials Science
Unmesh Ghorai: Tata Institute of Fundamental Research
Yuval Gefen: Weizmann Institute of Science
G. J. Sreejith: Indian Institute of Science Education and Research
Aveek Bid: Indian Institute of Science

Nature Communications, 2024, vol. 15, issue 1, 1-7

Abstract: Abstract Fractional quantum Hall (FQH) phases emerge due to strong electronic interactions and are characterized by anyonic quasiparticles, each distinguished by unique topological parameters, fractional charge, and statistics. In contrast, the integer quantum Hall (IQH) effects can be understood from the band topology of non-interacting electrons. We report a surprising super-universality of the critical behavior across all FQH and IQH transitions. Contrary to the anticipated state-dependent critical exponents, our findings reveal the same critical scaling exponent κ = 0.41 ± 0.02 and localization length exponent γ = 2.4 ± 0.2 for fractional and integer quantum Hall transitions. From these, we extract the value of the dynamical exponent z ≈ 1. We have achieved this in ultra-high mobility trilayer graphene devices with a metallic screening layer close to the conduction channels. The observation of these global critical exponents across various quantum Hall phase transitions was masked in previous studies by significant sample-to-sample variation in the measured values of κ in conventional semiconductor heterostructures, where long-range correlated disorder dominates. We show that the robust scaling exponents are valid in the limit of short-range disorder correlations.

Date: 2024
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DOI: 10.1038/s41467-024-52927-w

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