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.

arXiv comment15 pages with 10 figures. Submitted to Physical Review B

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• Microscopic Study of Edge Excitations of Spin-Polarized and Spin-Unpolarized $\nu =2/3$ Fractional Quantum Hall Effect
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• Chiral Luttinger liquids and a generalized Luttinger's theorem in fractional quantum Hall edges via finite-entanglement scaling
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• Many-body study of a quantum point contact in the fractional quantum Hall regime at v=5/2
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• Entropy-Enhanced Fractional Quantum Anomalous Hall Effect
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• Refermionized theory of the edge modes of a fractional quantum Hall cloud
• The Universal Edge Physics in Fractional Quantum Hall Liquids