Stability of even-denominator fractional quantum Hall states in systems with strong Landau-level mixing

TL;DR

This paper investigates the stability of even-denominator fractional quantum Hall states in systems with strong Landau-level mixing, explaining experimental results and predicting phase transitions and new states in materials like black phosphorene.

Contribution

It introduces a comprehensive approach incorporating screening and thickness effects to explain experimental observations and predicts the existence of fractional quantum Hall states in new materials.

Findings

Incompressibility at filling factor 5/2 can be unstable in strongly Landau-level-mixed systems.

Phase transitions are identifiable through the lowest collective mode gap when tuning magnetic field and well width.

Potential observation of even-denominator fractional quantum Hall effects in black phosphorene.

Abstract

Mixing of Landau levels has been understood to be essential in governing the nature of the ground state for the even-denominator fractional quantum Hall effect. The incompressibility of the ground state at filling factor $5/2$ in the strong Landau-level-mixed systems, such as the ZnO quantum well, is not always stable. Here we present an approach to generally deal with this kind of systems and satisfactorily explain the recent experiments [Falson \textit{et al}. Sci. Adv. \textbf{4}, eaat8742 (2018)] by implementing the screening plus the thickness effect. Further, the phase diagrams of the incompressibility of the ground state indicate that the phase transitions can be explicitly extracted by observing the lowest gap of the collective modes when the magnetic field and the width of the quantum well are tuned. We also predict the incompressibility of the two-dimensional electron gas in higher Landau levels in another strong Landau-level-mixed system, viz., the black phosphorene, by considering the screening effect where the relevant even-denominator fractional quantum Hall effects can possibly be observed.