Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-05-15
Int.J.Geom.Meth.Mod.Phys.7:143-164,2010
Physics
High Energy Physics
High Energy Physics - Theory
20 pages
Scientific paper
10.1142/S0219887810003975
We quantum mechanically analyze the fractional quantum Hall effect in graphene. This will be done by building the corresponding states in terms of a potential governing the interactions and discussing other issues. More precisely, we consider a system of particles in the presence of an external magnetic field and take into account of a specific interaction that captures the basic features of the Laughlin series \nu={1\over 2l+1}. We show that how its Laughlin potential can be generalized to deal with the composite fermions in graphene. To give a concrete example, we consider the SU(N) wavefunctions and give a realization of the composite fermion filling factor. All these results will be obtained by generalizing the mapping between the Pauli--Schr\"odinger and Dirac Hamiltonian's to the interacting particle case. Meantime by making use of a gauge transformation, we establish a relation between the free and interacting Dirac operators. This shows that the involved interaction can actually be generated from a singular gauge transformation.
Jellal Ahmed
Malika Bellati
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