Traits and characteristics of interacting Dirac fermions in monolayer and bilayer graphene

• Discuss properties of Dirac fermions in monolayer graphene.
• Discuss properties of Dirac fermions in bilayer graphene.
• Discuss properties of biased bilayer graphene.
• Bilayer graphene in a tilted magnetic field.
• Discuss the Pfaffians in graphene.

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.