Missing fractional quantum Hall states in ZnO

We have analyzed the crucial role a proper form of the Coulomb interaction 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 the 9/2 state in ZnO. Additionally, our study also reveals a strong presence of spin-reversed excitations in the 7/2 state in accordance with the experimental observation.