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

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.

5 pages, 4 figures, accepted for publication as a rapid communication in PRB

References in corpus (15)

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• Electromagnetic response and effective gauge theory of graphene in a magnetic field
• Controllable, driven phase transitions in the Fractional quantum Hall states in bilayer graphene
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• Pfaffian States in Coupled Atom-Cavity Systems
• Disappearence of the Aharonov-Bohm Effect for Interacting Electrons in a ZnO Quantum Ring

Cited by in corpus (10)

• Fractional charge and fractional statistics in the quantum Hall effects
• Comment on S. H. Simon, Interpretation of thermal conductance of the $\nu =5/2$ edge, arXiv:1801.09687
• Numerical exploration of trial wave functions for the particle-hole-symmetric Pfaffian
• A cascade of phase transitions in an orbitally mixed half-filled Landau level
• The sixteenfold way and the quantum Hall effect at half-integer filling factors
• PH-Pfaffian order in a translationally and rotationally invariant system
• Fractional quantum Hall effect at the filling factor $\nu =5/2$
• Tuning the Topological Features of Quantum-Dot Hydrogen and Helium by a Magnetic Field
• Phase transitions and topological properties of the 5/2 quantum Hall states with strong Landau-level mixing
• Exploring Quantum Hall Physics at Ultra-Low Temperatures and at High Pressures