Fractional quantum Hall edge: Effect of nonlinear dispersion and edge roton

Abstract

According to Wen's theory, a universal behavior of the fractional quantum Hall edge is expected at sufficiently low energies, where the dispersion of the elementary edge excitation is linear. A microscopic calculation shows that the actual dispersion is indeed linear at low energies, but deviates from linearity beyond certain energy, and also exhibits an "edge roton minimum." We determine the edge exponent from a microscopic approach, and find that the nonlinearity of the dispersion makes a surprisingly small correction to the edge exponent even at energies higher than the roton energy. We explain this insensitivity as arising from the fact that the energy at maximum spectral weight continues to show an almost linear behavior up to fairly high energies. We also formulate an effective field theory to describe the behavior of a reconstructed edge, taking into account multiple edge modes. Experimental consequences are discussed.

15 pages with 10 figures. Submitted to Physical Review B

References in corpus (6)

• Universal theory of nonlinear Luttinger liquids
• Phenomenology of One-Dimensional Quantum Liquids Beyond the Low-Energy Limit
• Monte Carlo simulation method for Laughlin-like states in a disk geometry
• Testing the topological nature of the fractional quantum Hall edge
• Semiconductor quantum dots in high magnetic fields: The composite-fermion view
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• Linear and nonlinear edge dynamics of trapped fractional quantum Hall droplets
• Edge properties of principal fractional quantum Hall states in the cylinder geometry
• Density matrix renormalization group study of the $\nu =1/3$ edge states in fractional quantum Hall systems
• Entropy-Enhanced Fractional Quantum Anomalous Hall Effect
• Entanglement spectrum edge reconstruction and correlation hole of the FQH liquids
• Thermoelectric Hall conductivity of the fractional quantum Hall systems on a disk
• Refermionized theory of the edge modes of a fractional quantum Hall cloud