Universality of Quantum Phase Transitions in the Integer and Fractional Quantum Hall Regimes

TL;DR

This study uncovers a universal critical behavior in both integer and fractional quantum Hall transitions, revealing identical scaling exponents across different regimes in ultra-high mobility graphene devices, challenging previous disorder-dependent variability.

Contribution

The paper demonstrates super-universality of quantum Hall transition critical exponents, showing they are consistent across integer and fractional regimes in short-range disorder conditions, using advanced graphene samples.

Findings

Same critical exponent $oxed{oxed{ ext{0.41} ext{±} ext{0.02}}}$ for all transitions.

Localization length exponent $oxed{oxed{ ext{2.4} ext{±} ext{0.2}}}$ consistent across regimes.

Dynamical exponent $z oxed{oxed{ ext{≈ 1}}}$ derived from scaling analysis.

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 $\kappa = 0.41 \pm 0.02$ and localization length exponent $\gamma = 2.4 \pm 0.2$ for fractional and integer quantum Hall transitions. From these, we extract the value of the dynamical exponent $z\approx 1$. 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 $\kappa$ 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.