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The recent discovery of fractional quantum Hall states in graphene raises thequestion of whether the physics of graphene and its bilayer offers anyadvantages over GaAs-based materials in exploring strongly-correlated states oftwo-dimensional electrons. Here we propose a method to continuously tune theeffective electron interactions in graphene and its bilayer by the dielectricenvironment of the sample. Using this method, the charge gaps of prominent FQHstates, including \nu=1/3 or \nu=5/2 states, can be increased several times, orreduced all the way to zero. The tunability of the interactions can be used torealize and stabilize various strongly correlated phases in the FQH regime, andto explore the transitions between them.

Tunable Electron Interactions and Fractional Quantum Hall States in Graphene