# The Pfaffian state in an electron gas with small Landau level gaps

## TL;DR

This paper investigates the impact of small Landau level gaps and screening effects on the Pfaffian state in ZnO, revealing potential topological phase transitions and the importance of system size and well width.

## Contribution

It introduces a model with screened Coulomb interaction to analyze the Pfaffian state in systems with small Landau level gaps, highlighting a possible topological phase transition.

## Key findings

- Overlap depends strongly on system size, indicating a new particle-hole symmetric Pfaffian ground state.
- Evidence of a topological phase transition between 2 and 3 in the ratio of Coulomb interaction to Landau level gap.
- Quantum well width and screening significantly influence the stability of the Pfaffian state.

## 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.