Traits and Characteristics of Interacting Dirac fermions in Monolayer and Bilayer Graphene

Abstract

The relativistic-like behavior of electrons in graphene significantly influences the interaction properties of these electrons in a quantizing magnetic field, resulting in more stable fractional quantum Hall effect states as compared to those in conventional (non-relativistic) semiconductor systems. In bilayer graphene the interaction strength can be controlled by a bias voltage and by the orientation of the magnetic field. The finite bias voltage between the graphene monolayers can in fact, enhance the interaction strength in a given Landau level. As a function of the bias voltage, a graphene bilayer system shows transitions from a state with weak electron-electron interactions to a state with strong interactions. Interestingly, the in-plane component of a tilted magnetic field can also alter the interaction strength in bilayer graphene. We also discuss the nature of the Pfaffian state in bilayer graphene and demonstrate that the stability of this state can be greatly enhanced by applying an in-plane magnetic field.

Invited Review: Solid State Communications, Special Issue on Graphene

References in corpus (14)

• The electronic properties of graphene
• Unconventional quantum Hall effect and Berry's phase of 2pi in bilayer graphene
• Asymmetry gap in the electronic band structure of bilayer graphene
• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Anyons and the quantum Hall effect - a pedagogical review
• 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
• Strained bilayer graphene: Band structure topology and Landau level spectrum
• Landau Level Quantization on the Sphere
• Controllable, driven phase transitions in the Fractional quantum Hall states in bilayer graphene
• Long range Coulomb interaction in bilayer graphene
• Collective Excitations of Dirac Electrons in Graphene

Cited by in corpus (20)

• The Effects of Landau level mixing on the fractional quantum Hall effect in monolayer Graphene
• Robust fractional quantum Hall effect and composite fermions in the $N=2$ Landau level in bilayer graphene
• Dynamical polarization and plasmons in a two-dimensional system with merging Dirac points
• Gap Structure of the Hofstadter System of Interacting Dirac Fermions in Graphene
• Aspects of Anisotropic Fractional Quantum Hall Effect in Phosphorene
• Understanding the Missing Fractional Quantum Hall States in ZnO
• Incompressible States of Dirac Fermions in Graphene with Anisotropic Interactions
• Effects of Interaction in the Hofstadter regime of the honeycomb lattice
• Interaction-Driven Distinctive Electronic States of Artificial Atoms at the ZnO Interface
• Tunability of the Fractional Quantum Hall States in Buckled Dirac Materials
• Persistence of gaps in the interacting Hofstadter model
• Statistical repulsion/attraction of electrons in graphene in a magnetic field
• Translational symmetry breaking and the disintegration of the Hofstadter butterfly
• Fractional Quantum Hall Effect in Hofstadter Butterflies of Dirac Fermions
• Thermodynamic properties of the electron gas in multilayer graphene in the presence of a perpendicular magnetic field
• Spin Transitions in Graphene Butterflies at an Integer Filling Factor
• Topological multiferroic phases in the extended Kane-Mele-Hubbard Model in the Hofstadter regime
• Seeking Maxwell's Demon in a non-reciprocal quantum ring
• Quantum Hall ferromagnets and transport properties of buckled Dirac materials
• Fractal Butterflies of Chiral Fermions in Bilayer Graphene: Phase Transitions and Emergent Properties