2008/05/31 by Ahmed Jellal, Bellati Malika, BELLATI MALIKA · 1 citation
Engineering · Materials Science · Mathematics · Physics and Astronomy · #Composite fermion #Condensed matter physics #Fractional quantum Hall effect #Graphene #Graphene research and applications #Low-power high-performance VLSI design #Magnetic field #Mathematical physics #Physics #Quantum Hall effect #Quantum and electron transport phenomena #Quantum mechanics #Quantum spin Hall effect #Theoretical physics #cond-mat.mes-hall #hep-th #math-ph #math.MP
paper · pdf · doi:10.1142/s0219887810003975
published as Int.J.Geom.Meth.Mod.Phys.7:143-164,2010 · 20 pages
openalex publication_date 2010/02/01 · arxiv created 2011/04/27 · arxiv updated 2011/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 [Formula: see text]. 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–Schrödinger 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.