Pfaffian state in an electron gas with small Landau level gaps

摘要

Landau level mixing plays an important role in the even denominator fractional quantum Hall states. InZnO the Landau level gap is essentially an order of magnitude smaller than that in a GaAs quantum well. Weintroduce the screened Coulomb interaction in a single Landau level to deal with that situation. Here we studythe incompressibility and the overlap of the ground state and the Pfaffian (or anti-Pfaffian) state at filling factors5/2 and 7/2 with a general screened Coulomb interaction. For small Landau level gaps, the overlap is stronglysystem size dependent and the screening can stabilize the incompressibility of the ground state with particle-holesymmetry which suggests a newly proposed particle-hole symmetry Pfaffian ground state. When the ratio ofCoulomb interaction to the Landau level gap κ varies, we find a possible topological phase transition in therange 2 < κ < 3, which was actually observed in an experiment. We then study how the width of quantum wellcombined with screening influences the system.