Theory of Competing Charge Density Wave, Kekule and Antiferromagnetic ordered Fractional Quantum Hall states in Graphene aligned with Boron Nitride

Abstract

We investigate spin and valley symmetry-broken fractional quantum Hall phases within a formalism that naturally extends the paradigm of quantum Hall ferromagnetism from integer to fractional quantum Hall states, allowing us to construct detailed phase diagrams for a large class of multi-component states. Motivated by recent experiments on Graphene aligned with a Boron Nitride substrate, we predict a sequence of transitions realized by increasing the magnetic field, starting from a sub-lattice polarized state to a valley coherent Kekule charge density wave state and further to an anti-ferromagnetic phase. Moreover for filling fractions such as $\nu =\pm 1/3$, we predict that the system undergoes a transition at low fields, that not only differ by the spin-valley orientation of the fractionally filled flavors but also by their intrinsic fractional quantum Hall nature. This transition is from a Laughlin-like state to a two component Halperin-like state both with a charge density wave order. Moreover for $\nu =\pm 1/3,\pm 2/3$, we predict a "canted Kekule density phase"(CaKD) where the spinors of integer and fractionally occupied components have different orientations in the valley Bloch sphere, in contrast to the Kekule state for the integer quantum Hall state at neutrality where both occupied components have the same orientation in the valley Bloch sphere.

16 pages, 7 figures

References in corpus (19)

• Quantum Hall Ferromagnetism in Graphene
• Observation of neutral modes in the fractional quantum Hall regime
• Observation of a Nematic Quantum Hall Liquid on the Surface of Bismuth
• Competing Nematic, Anti-ferromagnetic and Spin-flux orders in the Ground State of Bilayer Graphene
• Composite Fermions and Broken Symmetries in Graphene
• Interaction corrections to the polarization function of graphene
• Spinful Composite Fermions in a Negative Effective Field
• Edge excitations of the canted antiferromagnetic phase of the $\nu =0$ quantum Hall state in graphene: a simplified analysis
• The Effects of Landau level mixing on the fractional quantum Hall effect in monolayer Graphene
• Chiral Symmetry Breaking and the Quantum Hall Effect in Monolayer Graphene
• SO(5) symmetry in the quantum Hall effect in graphene
• Extracting net current from an upstream neutral mode in the fractional quantum Hall regime
• Abelian and Non-Abelian States in $\nu =2/3$ Bilayer Fractional Quantum Hall Systems
• Fractional quantum Hall effect in CVD-grown graphene
• Skyrmion zoo in graphene at charge neutrality in a strong magnetic field
• Microscopic Study of Edge Excitations of Spin-Polarized and Spin-Unpolarized $\nu =2/3$ Fractional Quantum Hall Effect
• Ground state and edge excitations of quantum Hall liquid at filling factor 2/3
• Fractional Hofstadter States in Graphene on Hexagonal Boron Nitride
• Integer Quantum Hall Effect of Interacting Electrons in Graphene