Higher-Spin Theory of the Magnetorotons

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 $2,3,\dots$. 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.

5 pages, 2 figures; v3: published version

References in corpus (4)

• Is the Composite Fermion a Dirac Particle?
• Experimental studies of the fractional quantum Hall effect in the first excited Landau level
• Splitting of Long-Wavelength Modes of the Fractional Quantum Hall Liquid at $\nu =1/3$
• Spontaneous polarization of composite fermions in the $n=1$ Landau level of graphene

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