Tunable electron interactions and fractional quantum Hall states in graphene

The recent discovery of fractional quantum Hall (FQH) states in graphene raises the question of whether the physics of graphene offers any advantages over GaAs-based materials in exploring strongly correlated states of two-dimensional electrons. Here we propose a method to continuously tune the effective electron interactions in graphene and its bilayer by the dielectric environment of the sample. Using this method, the charge gaps of prominent FQH states, including ν=1/3 or ν=5/2 states, can be increased several times, or reduced to zero. The tunability of the interactions can be used to realize and stabilize various strongly correlated phases and explore the transitions between them.