Positions of the magneto-roton minima in the fractional quantum Hall effect

The minima in the dispersion of the neutral excitation, which is a composite fermion exciton, are called “magneto-roton” minima. Golkar \emph{et al.}[1] have predicted the positions of the magneto-roton minima at filling factors $s/(2s+1)$ by treating the excitation as a deformation of the parent composite fermion Fermi sea at $1/2$. We use the composite fermion theory to calculate the exciton dispersion for different filling factors up to $5/11$, and find the positions of the first few magneto-roton minima agree well with Golkar \emph{et al.}’s predictions. Furthermore, we test the prediction that the positions of magneto-roton minima are insensitive to the microscopic form of the interaction by applying two different interactions in our calculation, namely the usual Columb interaction and the effective interaction in the $n=1$ Landau level of graphene. We see the positions of magneto-roton minima are nearly unchanged with these two different interactions.\\ [1] Golkar \emph{et al.} cond-mat arXiv:1602.08499