A unifying model for several two-dimensional phase transitions

Abstract

A relatively simple and physically transparent model based on quantum percolation and dephasing is employed to construct a global phase diagram which encodes and unifies the critical physics of the quantum Hall, "two-dimensional metal-insulator", classical percolation and, to some extent, superconductor-insulator transitions. Using real space renormalization group techniques, crossover functions between critical points are calculated. The critical behavior around each fixed point is analyzed and some experimentally relevant puzzles are addressed.

4 pages, including 3 figures

References in corpus (16)

• Metallic behavior and related phenomena in two dimensions
• Scaling Theory of the Integer Quantum Hall Effect
• Dissipation effects on the superconductor-insulator transition in 2-D superconductors
• Transport Through Quantum Melts
• Percolation-type description of the metal-insulator transition in two dimensions
• A New Transport Regime in the Quantum Hall Effect
• Effects of dissipation on quantum phase transitions
• The Quantized Hall Insulator: A New Insulator in Two-Dimensions
• A New Liquid Phase and Metal-Insulator Transition in Si MOSFETs
• Absence of Scaling in the Integer Quantum Hall Effect
• Localization and conductance fluctuations in the integer quantum Hall effect: Real--space renormalization group approach
• Hall Resistivity and Dephasing in the Quantum Hall Insulator
• 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
• Quantum Hall Criticality, Superconductor-Insulator Transition and Quantum Percolation
• Conductance distribution between Hall plateaus

Cited by in corpus (13)

• The Quantum Hall Transition in Real Space: From Localized to Extended States
• Two-dimensional superconductor-insulator quantum phase transitions in an electron-doped cuprate
• Thickness-tuned Superconductor-to-Insulator Transitions under magnetic field in a-NbSi
• Island formation in disordered superconducting thin films at finite magnetic fields
• Quantum criticality at the Chern-to-normal insulator transition
• From insulator to quantum Hall liquid at low magnetic fields
• Magnetic field tuned superconductor-to-insulator transition at the LaAlO${}_3$ /SrTiO${}_3$ interface
• Evidence of spatial inhomogeneity near the onset of magnetically induced insulating state in superconducting thin films
• Local Current Distribution and "Hot Spots" in the Integer Quantum Hall Regime
• Continuous and reversible tuning of the disorder-driven superconductor-insulator transition in bilayer graphene
• Probing onset of strong localization and electron-electron interactions with the presence of direct insulator-quantum Hall transition
• Angular dependence of the magnetic-field driven superconductor-insulator transition in thin films of amorphous indium-oxide
• Insulator, semiclassical oscillations and quantum Hall liquids at low magnetic fields