Competition between fractional quantum Hall liquid and electron solid phases in the Landau levels of multilayer graphene

Abstract

We study the competition between the electron liquid and solid phases, such as Wigner crystal and bubbles, in partially filled Landau levels (LLs) of multilayer graphene. Graphene systems offer a versatile platform for controlling band dispersion by varying the number of its stacked layers. The band dispersion determines the LL wave functions, and consequently, the LL-projected Coulomb interaction in graphene and its multilayers is different from that in conventional semiconductors like GaAs. As a result, the energies of the liquid and solid phases are different in the different LLs of multilayer graphene, leading to an alternative phase diagram for the stability of these phases, which we work out. The phase diagram of competing solid and liquid phases in the LLs of monolayer graphene has been studied previously. Here, we primarily consider $AB-$ or Bernal$-$stacked bilayer graphene (BLG) and $ABC-$stacked trilayer graphene (TLG) and focus on the Laughlin fractions. We determine the cohesive energy of the solid phase using the Hartree-Fock approximation, and the energy of the Laughlin liquid is computed analytically via the plasma sum rules. We find that at the Laughlin fillings, the electron liquid phase has the lowest energy among the phases considered in the $\mathcal{N}=0,1,2$ LLs of BLG, as well as in the $\mathcal{N}=3,4$ LLs of TLG, while in the $\mathcal{N}>2$ LLs of BLG and $\mathcal{N}>4$ LLs of TLG, the solid phases are more favorable. We also discuss the effect of impurities on the above-mentioned phase diagram.

27 pages, 37 figures

References in corpus (34)

• The electronic properties of graphene
• Biased bilayer graphene: semiconductor with a gap tunable by electric field effect
• Unconventional Integer Quantum Hall effect in graphene
• The electronic properties of bilayer graphene
• Quantum Hall Ferromagnetism in Graphene
• Electronic states and Landau levels in graphene stacks
• Multicomponent fractional quantum Hall effect in graphene
• Dependence of band structures on stacking and field in layered graphene
• Determination of the electronic structure of bilayer graphene from infrared spectroscopy results
• Chiral Decomposition in the Electronic Structure of Graphene Multilayers
• Graphene integer quantum Hall effect in the ferromagnetic and paramagnetic regimes
• Electron interactions in graphene in a strong magnetic field
• Composite Fermions and Broken Symmetries in Graphene
• Thirty Years of Composite Fermions and Beyond
• Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions
• Melting of a 2D Quantum Electron Solid in High Magnetic Field
• Order from Disorder in Graphene Quantum Hall Ferromagnet
• Competition between quantum-liquid and electron-solid phases in intermediate Landau levels
• The Effects of Landau level mixing on the fractional quantum Hall effect in monolayer Graphene
• Recent Experimental Progress of Fractional Quantum Hall Effect: 5/2 Filling State and Graphene
• Evidence for Two Different Solid Phases of Two Dimensional Electrons in High Magnetic Fields
• Parton construction of particle-hole-conjugate Read-Rezayi parafermion fractional quantum Hall states and beyond
• Microscopic Theory of the Reentrant IQHE in the First and Second Excited LLs
• Abelian and Non-Abelian States in $\nu =2/3$ Bilayer Fractional Quantum Hall Systems
• A non-Abelian fractional quantum Hall state at $3/7$ filled Landau level
• Unconventional ${\mathbb{Z}}_n$ parton states at $\nu =7/3$: The role of finite width
• De-Pinning Transition of Bubble Phases in a High Landau Level
• Influence of Landau-level mixing on Wigner crystallization in graphene
• Nonequilibrium transport in density-modulated phases of the second Landau level
• A Highly Correlated Topological Bubble Phase of Composite Fermions
• Scaling Approach to the Phase Diagram of Quantum Hall Systems
• Magnetoroton instabilities and static susceptibilities in higher Landau levels
• Prediction of non-Abelian fractional quantum Hall effect at $\nu =2+\frac{4}{11}$
• Phase diagram of the $\nu =2$ quantum Hall state in bilayer graphene

Cited by in corpus (8)

• Anomalous Hall Crystals in Rhombohedral Multilayer Graphene II: General Mechanism and a Minimal Model
• Fractional quantum Hall coexistence phases in higher Landau levels of graphene
• Magnetic and Lattice Ordered Fractional Quantum Hall Phases in Graphene
• Static structure factor and the dispersion of the Girvin-MacDonald-Platzman density mode for fractional quantum Hall fluids on the Haldane sphere
• Universal Modelling of Oscillations in Fractional Quantum Hall Fluids
• Hetero-Orbital Two-Component Fractional Quantum Hall States in Bilayer Graphene
• Interaction-driven quantum phase transitions between topological and crystalline orders of electrons
• Dispersion of collective modes in spinful fractional quantum Hall states on the sphere