Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2009-09-08
J.Math.Phys.51:063522,2010
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
14 pages, 1 figure, paper extended, new references added. Version to appear in JMP
Scientific paper
A generalized algebra of noncommutative coordinates and momenta embracing non-Abelian gauge fields is proposed. Through a two-dimensional realization of this algebra for a gauge field including electromagnetic vector potential and two spin-orbit-like coupling terms, a Dirac-like Hamiltonian in noncommutative coordinates is introduced. We established the corresponding energy spectrum and from that we derived the relation between the energy level quantum number and the magnetic field at the maxima of Shubnikov-de Haas oscillations. By tuning the non-commutativity parameter \theta in terms of the values of magnetic field at the maxima of Shubnikov-de Haas oscillations we accomplished the experimentally observed Landau plot of the peaks for graphene. Accepting that the experimentally observed behavior is due to the confinement of carriers, we conclude that our method of introducing noncommutative coordinates provides another formulation of the confined massless Dirac fermions in graphene.
Dayi Omer F.
Jellal Ahmed
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