Pfaffian state in an electron gas with small Landau level gaps

Abstract

Landau level mixing plays an important role in the even denominator fractional quantum Hall 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 deal with that situation. Here we study the incompressibility and the overlap of the ground state and the Pfaffian (or anti-Pfaffian) state at filling factors $\frac{5}{2}$ and $\frac{7}{2}$ with a general screened Coulomb interaction. For small Landau level gaps, the overlap is strongly system size dependent and the screening can stabilize the incompressibility of the ground state with particle-hole symmetry which suggests a newly proposed particle-hole symmetry Pfaffian ground state. When the ratio of Coulomb interaction to the Landau level gap $\ensuremath{\kappa}$ varies, we find a possible topological phase transition in the range $2<\ensuremath{\kappa}<3$, which was actually observed in an experiment. We then study how the width of quantum well combined with screening influences the system.