Universality of the edge tunneling exponent of fractional quantum Hall liquids

Abstract

Recent calculations of the edge tunneling exponents in quantum Hall states appear to contradict their topological nature. We revisit this issue and find no fundamental discrepancies. In a microscopic model of fractional quantum Hall liquids with electron-electron interaction and confinement, we calculate the edge Green's function via exact diagonalization. Our results for $\nu =1/3$ and 2/3 suggest that in the presence of Coulomb interaction, the sharpness of the edge and the strength of the edge confining potential, which can lead to edge reconstruction, are the parameters that are relevant to the universality of the electron tunneling I-V exponent.

5 pages, 3 figures

References in corpus (4)

• Edge reconstruction in the fractional quantum Hall regime
• Field Theoretical Description of Quantum Hall Edge Reconstruction
• Relevance of inter-composite fermion interaction to the edge Tomonaga-Luttinger liquid
• Edge reconstructions in fractional quantum Hall systems

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• Edge properties of principal fractional quantum Hall states in the cylinder geometry
• Electron operator at the edge of the 1/3 fractional quantum Hall liquid
• Microscopic study of the 2/5 fractional quantum Hall edge
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• Mechanism for particle fractionalization and universal edge physics in quantum Hall fluids
• Incidence of the boundary shape in the effective theory of fractional quantum Hall edges
• The Monte Carlo simulation of the topological quantities in FQH systems
• Universal Modelling of Oscillations in Fractional Quantum Hall Fluids
• Explicit mapping between a 2D quantum Hall system and a 1D Luttinger liquid. II. Correlation functions
• Fractional charge revealed in computer simulations of resonant tunneling in the fractional quantum Hall regime
• Many-body study of a quantum point contact in the fractional quantum Hall regime at v=5/2
• Quantum Hall droplet laterally coupled to a quantum ring
• The Tomonaga-Luttinger Model and the Chern-Simons Theory for the Edges of Multi-layer Fractional Quantum Hall Systems
• The length scale measurements of the Fractional quantum Hall state on cylinder
• Universality Lost: Relation between quantizations of the Hall conductance and the edge exponents in fractional quantum Hall effect
• The Universal Edge Physics in Fractional Quantum Hall Liquids
• Edge reconstruction of compressible Quantum Hall fluid in the filling fraction range 1/3 to 2/3
• Effects of interaction induced second Landau level mixing in the nu=1 quantum Hall effect
• Collapse of edge reconstruction in compressible Quantum Hall fluid within filling fraction range 2/3 to 1