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

TL;DR

This paper investigates the nonlinear dispersion of fractional quantum Hall edges, revealing that nonlinearity has minimal impact on edge exponents and discussing implications for reconstructed edges and experiments.

Contribution

It provides a microscopic calculation of edge dispersion showing deviations from linearity and introduces an effective field theory for reconstructed edges.

Findings

Edge dispersion deviates from linearity beyond low energies.

Nonlinear dispersion has a small effect on edge exponents.

Effective field theory accounts for multiple edge modes.

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.