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 (21)

• Continuous Quantum Phase Transitions
• Scaling Theory of the Integer Quantum Hall Effect
• The hot pick-up technique for batch assembly of van der Waals heterostructures
• Correlated Insulator and Chern Insulators in Pentalayer Rhombohedral Stacked Graphene
• Scaling in Plateau-to-Plateau Transition: A Direct Connection of Quantum Hall Systems with Anderson Localization Model
• Landau Level Mixing and the Fractional Quantum Hall Effect
• Landau level spectra and the quantum Hall effect of multilayer graphene
• Hopping conductivity in the quantum Hall effect -- revival of universal scaling
• Emergent Dirac gullies and gully-symmetry breaking quantum Hall states in ABA trilayer graphene
• New Dirac points and multiple Landau level crossings in biased trilayer graphene
• Tunable interactions and phase transitions in Dirac materials in a magnetic field
• Integer quantum Hall effect of interacting electrons: dynamical scaling and critical conductivity
• Dynamical scaling of the quantum Hall plateau transition
• Role of different scattering mechanisms on the temperature dependence of transport in graphene
• Widely Tunable Quantum Phase Transition from Moore-Read to Composite Fermi Liquid in Bilayer Graphene
• Particle-Hole Symmetry and the Fractional Quantum Hall Effect in the Lowest Landau Level
• Anderson localization in fractional quantum Hall effect
• Spontaneous Gully Polarized Quantum Hall States in ABA Trilayer Graphene
• Interaction effects on quantum Hall transitions: dynamical scaling laws and superuniversality
• Gully quantum Hall ferromagnetism in biased trilayer graphene
• Delocalization and Universality of the Fractional Quantum Hall Plateau-to-Plateau Transitions

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