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

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.

42 pages

References in corpus (7)

• Correlated Insulator and Chern Insulators in Pentalayer Rhombohedral Stacked Graphene
• New Dirac points and multiple Landau level crossings in biased trilayer graphene
• Dynamical scaling of the quantum Hall plateau transition
• Anderson localization in fractional quantum Hall effect
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Cited by in corpus (6)

• Topological physics in quantum critical systems
• Tunable Band Inversion in Trilayer Graphene
• Quasi-${\Phi }_0$-periodic supercurrent at quantum Hall transitions
• Cascade of fractional quantum Hall states in 2D system
• The impact of dimensionality on universality of quantum Hall transitions
• Even-denominator fractional quantum Hall states in the zeroth Landau level of ABA trilayer graphene