A noncommutative space approach to confined Dirac fermions in graphene

Dayı Ö. F., JELLAL A.

JOURNAL OF MATHEMATICAL PHYSICS, vol.51, no.6, 2010 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 51 Issue: 6
  • Publication Date: 2010
  • Doi Number: 10.1063/1.3442719
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Istanbul Technical University Affiliated: Yes


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 noncommutativity 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. (C) 2010 American Institute of Physics. [doi:10.1063/1.3442719]