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

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. In this talk, I will 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...