  We have analyzed the crucial role the Coulomb interaction strength plays on
the even and odd denominator fractional quantum Hall effects in a
two-dimensional electron gas (2DEG) in the ZnO heterointerface. In this system,
the Landau level gaps are much smaller than those in conventional GaAs systems.
The Coulomb interaction is also very large compared to the Landau level gap
even in very high magnetic fields. We therefore consider the influence of
higher Landau levels by considering the screened Coulomb potential in the
random phase approximation. Interestingly, our exact diagonalization studies of
the collective modes with this screened potential successfully explain recent
experiments of even and odd denominator fractional quantum Hall effects, in
particular, the unexpected absence of the 5/2 state and the presence of 9/2
state in ZnO.
