A partially filled Landau level (LL) hosts a variety of correlated states of matter with unique properties. The ability to control these phases requires tuning the effective electron interactions within a LL, which has been difficult to achieve in GaAs-based structures. Here we consider a class of Dirac materials in which the chiral band structure, along with the mass term, gives rise to a wide tunability of the effective interactions by the magnetic field. This tunability is such that different phases can occur in a single LL, and phase transitions between them can be driven in situ. The incompressible, Abelian and non-Abelian, liquids are stabilized in interaction regimes different from GaAs. Our study points to a realistic method of controlling the correlated phases and studying the phase transitions between them in materials such as graphene, bilayer graphene, and topological insulators.

• Received 28 November 2011

DOI:https://doi.org/10.1103/PhysRevB.84.241306