The Effects of Landau level mixing on the fractional quantum Hall effect in monolayer Graphene

Abstract

We report results of exact diagonalization studies of the spin- and valley-polarized fractional quantum Hall effect in the $N=0$ and 1 Landau levels in graphene. We use an effective model that incorporates Landau level mixing to lowest-order in the parameter $\kappa =\frac{e^2/\epsilon \ell }{\hslash v_F/\ell }=\frac{e^2}{\epsilon v_F\hslash }$ which is magnetic field independent and can only be varied through the choice of substrate. We find Landau level mixing effects are negligible in the $N=0$ Landau level for $\kappa \lesssim 2$. In fact, the lowest Landau level projected Coulomb Hamiltonian is a better approximation to the real Hamiltonian for graphene than it is for semiconductor based quantum wells. Consequently, the principal fractional quantum Hall states are expected in the $N=0$ Landau level over this range of $\kappa$. In the $N=1$ Landau level, fractional quantum Hall states are expected for a smaller range of $\kappa$ and Landau level mixing strongly breaks particle-hole symmetry producing qualitatively different results compared to the $N=0$ Landau level. At half-filling of the $N=1$ Landau level, we predict the anti-Pfaffian state will occur for $\kappa \sim 0.25$-$0.75$.

4 pages, 3 figures; v2 is published version with additional references

References in corpus (11)

• Non-Abelian Anyons and Topological Quantum Computation
• Quantum Hall Ferromagnetism in Graphene
• Multicomponent fractional quantum Hall effect in graphene
• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Electron interactions in graphene in a strong magnetic field
• The Fractional Quantum Hall States of Dirac Electrons in Graphene
• Fractional Quantum Hall Effect in Graphene
• Pseudopotentials for Multi-particle Interactions in the Quantum Hall Regime
• Long range Coulomb interaction in bilayer graphene
• Theoretical expectations for a fractional quantum Hall effect in graphene

Cited by in corpus (25)

• Composite Fermions and Broken Symmetries in Graphene
• Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions
• Thirty Years of Composite Fermions and Beyond
• Imaging tunable quantum Hall broken-symmetry orders in graphene
• Composite fermion duality for half-filled multicomponent Landau Levels
• The Most General Form of Deformation of the Heisenberg Algebra from the Generalized Uncertainty Principle
• Microscopic Model for Fractional Quantum Hall Nematics
• Composite fermion pairing induced by Landau level mixing
• Fractional Quantum Hall State at Filling Factor $\nu =1/4$ in Ultra-High-Quality GaAs 2D Hole Systems
• Global phase diagram of charge neutral graphene in the quantum Hall regime for generic interactions
• Theory of Competing Charge Density Wave, Kekule and Antiferromagnetic ordered Fractional Quantum Hall states in Graphene aligned with Boron Nitride
• Revisiting excitation gaps in the fractional quantum Hall effect
• Competition between fractional quantum Hall liquid and electron solid phases in the Landau levels of multilayer graphene
• Absence of heat flow in ν = 0 quantum Hall ferromagnet in bilayer graphene
• Tilt-Induced Phase Transitions in Even-Denominator Fractional Quantum Hall States at the ZnO Interface
• Vanishing bulk heat flow in the nu=0 quantum Hall ferromagnet in monolayer graphene
• Magnetic and Lattice Ordered Fractional Quantum Hall Phases in Graphene
• Fractional quantum Hall coexistence phases in higher Landau levels of graphene
• Competing Many-Body Phases at Small Fillings in Ultrahigh-Quality GaAs 2D Hole Systems: Role of Landau Level Mixing
• Developing fractional quantum Hall states at $\nu$ = $\frac{1}{7}$ and $\frac{2}{11}$ in the presence of significant Landau level mixing
• Phase transitions and topological properties of the 5/2 quantum Hall states with strong Landau-level mixing
• Fractional quantum Hall effect in bilayer graphene beyond the single Landau level approximation
• Collective excitations of fractional quantum Hall states in monolayer graphene
• Uniquely identifying quantum Hall phases in charge neutral graphene
• Study of polarization of even-denominator fractional quantum Hall states in SU(4) Graphene