Title: The Pfaffian state in an electron gas with small Landau level gaps,
Abstract: Landau level mixing plays an important role in the Pfaffian (or
anti-Pfaffian) states. In ZnO the Landau level gap is essentially an order of
magnitude smaller than that in a GaAs quantum well. We introduce the screened
Coulomb interaction in a single Landau level to tackle that situation. Here we
study the overlap of the ground state and the Pfaffian (or anti-Pfaffian) state
at evendenominator fractional quantum Hall (FQH) states present in ZnO. The
overlap is strongly system size-dependent which suggests a newly proposed
particle-hole symmetry Pfaffian ground state in the extreme Landau level mixing
limit. When the ratio of Coulomb interaction to the Landau level gap \k{appa}
varies, we find a possible topological phase transition in the range 2 <
\k{appa} < 3, which was actually observed in an experiment. We then study how
the width of quantum well combined with screening influences the overlap.