Speaker
Description
Fractional quantum Hall liquids exhibit a rich set of excitations, the
lowest-energy of which are the magneto-rotons with dispersion minima
at finite momentum. We propose a theory of the magneto-rotons 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,... The mixing of modes at nonzero momentum
$q$ leads to the characteristic bending down of the lowest excitation
and the appearance of the magneto-roton minima. A purely algebraic
argument show that the magneto-roton 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.
