Cascade of Quantum Phase Transitions in Tunnel-Coupled Edge States

Abstract

We report on the cascade of quantum phase transitions exhibited by tunnel-coupled edge states across a quantum Hall line junction. We identify a series of quantum critical points between successive strong and weak tunneling regimes in the zero-bias conductance. Scaling analysis shows that the conductance near the critical magnetic fields $B_c$ is a function of a single scaling argument $|B-B_c|T^{-\kappa }$, where the exponent $\kappa =0.42$. This puzzling resemblance to a quantum Hall-insulator transition points to importance of interedge correlation between the coupled edge states.

4 pages, 3 figures

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• Inter-edge interactions and novel fixed points at a junction of quantum Hall line junctions
• The Jain-2/5 parent Hamiltonian: structure of zero modes, dominance patterns, and zero mode generators
• Line junction in a quantum Hall system with two filling fractions
• Momentum resolved tunneling into the Pfaffian and anti-Pfaffian edges
• Edge State Tunneling in a Split Hall Bar Model
• Quantum interference and spin-charge separation in a disordered Luttinger liquid
• Topologically ordered zigzag nanoribbon: $e/2$ fractional edge charge, spin-charge separation, and ground state degeneracy
• Quasi-particle tunneling at a constriction in a fractional quantum Hall state
• Edge Magnetoplasmons in Quantum Hall Line Junction Systems
• Electron Spectral Functions of Reconstructed Quantum Hall Edges
• Tunneling in Fractional Quantum Hall line junctions
• Zero-Bias Anomalies in Narrow Tunnel Junctions in the Quantum Hall Regime
• Calculation and spectroscopy of the Landau band structure at a thin and atomically precise tunneling barrier
• Electrostatics of Edge States of Quantum Hall Systems with Constrictions: Metal--Insulator Transition Tuned by External Gates
• AC conductivity of a quantum Hall line junction
• Tunneling between Two Quantum Hall Droplets
• Laterally coupled and field-induced quantum Hall systems