An experimental study on $\Gamma$(2) modular symmetry in the quantum Hall system with a small spin-splitting

Abstract

Magnetic-field-induced phase transitions were studied with a two-dimensional electron AlGaAs/GaAs system. The temperature-driven flow diagram shows the features of the $\Gamma$(2) modular symmetry, which includes distorted flowlines and shiftted critical point. The deviation of the critical conductivities is attributed to a small but resolved spin splitting, which reduces the symmetry in Landau quantization. [B. P. Dolan, Phys. Rev. B 62, 10278.] Universal scaling is found under the reduction of the modular symmetry. It is also shown that the Hall conductivity could still be governed by the scaling law when the semicircle law and the scaling on the longitudinal conductivity are invalid. *corresponding author:[email protected]

The revised manuscript has been published in J. Phys.: Condens. Matter

References in corpus (18)

• Continuous Quantum Phase Transitions
• A New Transport Regime in the Quantum Hall Effect
• Collapse of Spin-Splitting in the Quantum Hall Effect
• A different view of the quantum Hall plateau-to-plateau transitions
• Critical Collapse of the Exchange Enhanced Spin Splitting in 2-D Systems
• Hopping conductivity in the quantum Hall effect -- revival of universal scaling
• Modular Invariance, Self-Duality and The Phase Transition Between Quantum Hall Plateaus
• Derivation of the Semi-circle Law from the Law of Corresponding States
• Semicircle: An exact relation in the Integer and Fractional Quantum Hall Effect
• Duality in the Quantum Hall Effect - the Role of Electron Spin
• Quantum criticality, particle-hole symmetry, and duality of the plateau-insulator transition in the quantum Hall regime
• A metallic phase in quantum Hall systems
• Direct measurements of the spin and the cyclotron gaps in a 2D electron system in silicon
• Quantum Breakdown of the Quantized Hall Insulator
• $\Gamma (2)$ modular symmetry, renormalization, group flow and the quantum Hall effect
• New Insights into the Plateau-Insulator Transition in the Quantum Hall Regime
• A study on the universality of the magnetic-field-induced phase transitions in the two-dimensional electron system in an AlGaAs/GaAs heterostructure
• Spin-splitting in the quantum Hall effect of disordered GaAs layers with strong overlap of the spin subbands

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