Quantum Hall Criticality, Superconductor-Insulator Transition and Quantum Percolation

Abstract

A model consisting of a mixture of superconducting and quantum links is proposed to describe the integer quantum Hall transition. The quantum links correspond to tunneling of electrons between trajectories trapped in adjacent potential valleys, while the superconducting links correspond to merging of these trajectories once the Fermi energy crosses the saddle point energy separating the two valleys. The quantum Hall transition in this model corresponds to percolation of the superconducting links. Numerical calculations and scaling analysis using two different approaches yield the critical exponent $\nu \approx 2.4$ and a two-peak conductance distribution at the critical point. The role of quantum coherence is discussed, and an explanation of experimental observations claiming different universality class for the quantum Hall transition is suggested. The model suggests that the critical behavior of the superconductor-insulator transition from the insulating side is in the same universality class as the quantum Hall transition.

References in corpus (12)

• Scaling Theory of the Integer Quantum Hall Effect
• Transport Through Quantum Melts
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• Anomalous proximity effect in an inhomogeneous disordered superconductor
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• Real Space Renormalization of the Chalker-Coddington Model
• Magneto-optical evidence of the percolation nature of the metal-insulator transition in the 2D electron system
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• Conductance distribution between Hall plateaus

Cited by in corpus (6)

• Universal Magnetic-Field-Driven Metal-Insulator-Metal Transformations in Graphite and Bismuth
• Theory of Magneto-resistance of Disordered Superconducting Films
• A unifying model for several two-dimensional phase transitions
• From insulator to quantum Hall liquid at low magnetic fields
• Local Current Distribution and "Hot Spots" in the Integer Quantum Hall Regime
• Diffusion and localization in quantum random resistor networks