Fractional Quantum Hall States in Graphene
May, 200820 pages
Published in:
- Int.J.Geom.Meth.Mod.Phys. 7 (2010) 143-164
e-Print:
- 0805.2388 [hep-th]
Report number:
- UCDTPG-08-01
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Abstract: (arXiv)
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.- Dirac Hamiltonian
- graphene
- Laughlin states
- SU(N) wavefunctions
- composite fermions
- transformation: gauge
- fermion: composite
- particle: interaction
- Hall effect: fractional
- operator: Dirac
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