Higher-Spin Theory of the Magnetorotons

TL;DR

This paper develops a theoretical framework for magnetoroton excitations in fractional quantum Hall liquids near half filling, revealing universal features and mode mixing effects that produce characteristic minima in the excitation spectrum.

Contribution

It introduces an infinite bosonic field theory based on Fermi surface fluctuations, predicting universal magnetoroton minima locations tied to Bessel function zeros.

Findings

Magnetoroton minima occur at specific momenta related to Bessel function zeros.

The theory predicts a spectrum with multiple neutral excitations of varying spins.

Minima locations are universal for Fermi surfaces coupled to gauge fields in magnetic fields.

Abstract

Fractional quantum Hall liquids exhibit a rich set of excitations, the lowest-energy of which are the magnetorotons with dispersion minima at a finite momentum. We propose a theory of the magnetorotons on the quantum Hall plateaux near half filling, namely, at filling fractions $\nu=N/(2N+1)$ at large $N$. The theory involves an infinite number of bosonic fields arising from bosonizing the fluctuations of the shape of the composite Fermi surface. At zero momentum there are $O(N)$ neutral excitations, each carrying a well-defined spin that runs integer values $2,3,\ldots$. The mixing of modes at nonzero momentum $q$ leads to the characteristic bending down of the lowest excitation and the appearance of the magnetoroton minima. A purely algebraic argument shows that the magnetoroton minima are located at $q\ell_B=z_i/(2N+1)$, where $\ell_B$ is the magnetic length and $z_i$ are the zeros of the Bessel function $J_1$, independent of the microscopic details. We argue that these minima are universal features of any two-dimensional Fermi surface coupled to a gauge field in a small background magnetic field.