A Noncommutative Space Approach to Confined Dirac Fermions in Graphene
arXiv:0909.1448 · doi:10.1063/1.3442719
Abstract
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 θin 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.
14 pages, 1 figure, paper extended, new references added. Version to appear in JMP
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Cited by in corpus (12)
- Dunkl-Graphene in constant magnetic field
- Graphene and non-Abelian quantization
- Electron dynamics in noncommutative geometry with magnetic field and Zitterbewegung phenomenon
- Noncommutativity in (2+1)-dimensions and the Lorentz group
- Non-Commutativity effects in the Dirac equation in crossed electric and magnetic fields
- An Alternative Formulation of Hall Effect and Quantum Phases in Noncommutative Space
- Tunneling in an anisotropic cubic Dirac semi-metal
- Exciton swapping in a twisted graphene bilayer as a solid-state realization of a two-brane model
- Black Holes Thermodynamics in a new kind of Noncommutative Geometry
- Landau levels for graphene layers in noncommutative plane
- Zitterbewegung in Noncommutative Geometry
- Thermal Properties of Gauge-Invariant Graphene in Noncommutative Phase-Space