Theory Of Fractional Quantum Hall Effect

This project is devoted to the investigation of the modern state of the problem connected withrnquantum Hall effect (integral and fractional). The quantum Hall effect is a quantum-mechanicalrnversion of the Hall effect, observed in two dimensional electron systems subjected to lowrntemperatures (< 11) and strong magnetic fields (∼ 104), in which the Hall conductance5( )rntakes on the quantized values(678rn9 ) with : an integer (integer quantized Hall effect) or a rationalrnfraction (fractional quantized Hall effect), independent of the detail of the sample geometry. inrnthis project we see detail description of fractional quantum hall effect by using some theories, Itrnstarts from the LAUGHLIN states and their generalization following JAIN’s picture of compositernfermions. The work of this project ends with a description of the fractional quantum hall effectrnin graphene, since graphene is two dimensional carbon and carbon atoms in graphene, showsrnelectron-electron interaction thus we must expect fractional quantum hall effect in graphene

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