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

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 system and satisfactorily explain the recent experiments [Falson et al., Sci. Adv. 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.

Automated summary

The mixing of Landau levels is crucial in determining the nature of the ground state in the fractional quantum Hall effect. The stability of the ground state at filling factor 5/2 in strong Landau-level-mixed systems is addressed, with a proposed approach involving screening and thickness effect explaining recent experiments. Phase diagrams show that phase transitions can be observed by tuning the magnetic field and quantum well width, with predictions for incompressibility in higher Landau levels in another mixed system.